Spectral Theory of the Riemann Zeta-Function

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Author :
Publisher : Cambridge University Press
ISBN 13 : 1316582507
Total Pages : 240 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Spectral Theory of the Riemann Zeta-Function by : Yoichi Motohashi

Download or read book Spectral Theory of the Riemann Zeta-Function written by Yoichi Motohashi and published by Cambridge University Press. This book was released on 1997-09-11 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Riemann zeta function is one of the most studied objects in mathematics, and is of fundamental importance. In this book, based on his own research, Professor Motohashi shows that the function is closely bound with automorphic forms and that many results from there can be woven with techniques and ideas from analytic number theory to yield new insights into, and views of, the zeta function itself. The story starts with an elementary but unabridged treatment of the spectral resolution of the non-Euclidean Laplacian and the trace formulas. This is achieved by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory as well. These ideas are then utilized to unveil an image of the zeta-function, first perceived by the author, revealing it to be the main gem of a necklace composed of all automorphic L-functions. In this book, readers will find a detailed account of one of the most fascinating stories in the development of number theory, namely the fusion of two main fields in mathematics that were previously studied separately.

Spectral Theory of the Riemann Zeta-Function

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Author :
Publisher : Cambridge University Press
ISBN 13 : 0521445205
Total Pages : 246 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Spectral Theory of the Riemann Zeta-Function by : Yoichi Motohashi

Download or read book Spectral Theory of the Riemann Zeta-Function written by Yoichi Motohashi and published by Cambridge University Press. This book was released on 1997-09-11 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Riemann zeta function is one of the most studied objects in mathematics, and is of fundamental importance. In this book, based on his own research, Professor Motohashi shows that the function is closely bound with automorphic forms and that many results from there can be woven with techniques and ideas from analytic number theory to yield new insights into, and views of, the zeta function itself. The story starts with an elementary but unabridged treatment of the spectral resolution of the non-Euclidean Laplacian and the trace formulas. This is achieved by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory as well. These ideas are then utilized to unveil an image of the zeta-function, first perceived by the author, revealing it to be the main gem of a necklace composed of all automorphic L-functions. In this book, readers will find a detailed account of one of the most fascinating stories in the development of number theory, namely the fusion of two main fields in mathematics that were previously studied separately.

Riemann Hypothesis and Spectral Theory

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Publisher :
ISBN 13 :
Total Pages : 343 pages
Book Rating : 4.4/5 (84 download)

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Book Synopsis Riemann Hypothesis and Spectral Theory by : Jason Cole

Download or read book Riemann Hypothesis and Spectral Theory written by Jason Cole and published by . This book was released on 2021-09-19 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a brief overview of the Riemann Zeta function, Riemann Hypothesis and the Hilbert-Polya spectral operator approach to proving RH. Also included in this book is a new discovery that describes a correlation between the Riemann Xi function and gravity rotational curves. Surprisingly their is a mathematical correlation between the complex system of the Riemann Xi function and the large scale distribution of galaxies and rotational curves. Also included in this book are new discoveries on the Prime Number theorem, Riemann Zeta function and other new science and math discoveries.

Dynamical, Spectral, and Arithmetic Zeta Functions

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Publisher : American Mathematical Soc.
ISBN 13 : 0821820796
Total Pages : 210 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Dynamical, Spectral, and Arithmetic Zeta Functions by : Michel Laurent Lapidus

Download or read book Dynamical, Spectral, and Arithmetic Zeta Functions written by Michel Laurent Lapidus and published by American Mathematical Soc.. This book was released on 2001 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The original zeta function was studied by Riemann as part of his investigation of the distribution of prime numbers. Other sorts of zeta functions were defined for number-theoretic purposes, such as the study of primes in arithmetic progressions. This led to the development of $L$-functions, which now have several guises. It eventually became clear that the basic construction used for number-theoretic zeta functions can also be used in other settings, such as dynamics, geometry, and spectral theory, with remarkable results. This volume grew out of the special session on dynamical, spectral, and arithmetic zeta functions held at the annual meeting of the American Mathematical Society in San Antonio, but also includes four articles that were invited to be part of the collection. The purpose of the meeting was to bring together leading researchers, to find links and analogies between their fields, and to explore new methods. The papers discuss dynamical systems, spectral geometry on hyperbolic manifolds, trace formulas in geometry and in arithmetic, as well as computational work on the Riemann zeta function. Each article employs techniques of zeta functions. The book unifies the application of these techniques in spectral geometry, fractal geometry, and number theory. It is a comprehensive volume, offering up-to-date research. It should be useful to both graduate students and confirmed researchers.

An Approach to the Selberg Trace Formula via the Selberg Zeta-Function

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Author :
Publisher : Springer
ISBN 13 : 3540393315
Total Pages : 188 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis An Approach to the Selberg Trace Formula via the Selberg Zeta-Function by : Jürgen Fischer

Download or read book An Approach to the Selberg Trace Formula via the Selberg Zeta-Function written by Jürgen Fischer and published by Springer. This book was released on 2006-11-15 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Notes give a direct approach to the Selberg zeta-function for cofinite discrete subgroups of SL (2,#3) acting on the upper half-plane. The basic idea is to compute the trace of the iterated resolvent kernel of the hyperbolic Laplacian in order to arrive at the logarithmic derivative of the Selberg zeta-function. Previous knowledge of the Selberg trace formula is not assumed. The theory is developed for arbitrary real weights and for arbitrary multiplier systems permitting an approach to known results on classical automorphic forms without the Riemann-Roch theorem. The author's discussion of the Selberg trace formula stresses the analogy with the Riemann zeta-function. For example, the canonical factorization theorem involves an analogue of the Euler constant. Finally the general Selberg trace formula is deduced easily from the properties of the Selberg zeta-function: this is similar to the procedure in analytic number theory where the explicit formulae are deduced from the properties of the Riemann zeta-function. Apart from the basic spectral theory of the Laplacian for cofinite groups the book is self-contained and will be useful as a quick approach to the Selberg zeta-function and the Selberg trace formula.

Quantized Number Theory, Fractal Strings And The Riemann Hypothesis: From Spectral Operators To Phase Transitions And Universality

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Publisher : World Scientific
ISBN 13 : 9813230819
Total Pages : 494 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Quantized Number Theory, Fractal Strings And The Riemann Hypothesis: From Spectral Operators To Phase Transitions And Universality by : Hafedh Herichi

Download or read book Quantized Number Theory, Fractal Strings And The Riemann Hypothesis: From Spectral Operators To Phase Transitions And Universality written by Hafedh Herichi and published by World Scientific. This book was released on 2021-07-27 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studying the relationship between the geometry, arithmetic and spectra of fractals has been a subject of significant interest in contemporary mathematics. This book contributes to the literature on the subject in several different and new ways. In particular, the authors provide a rigorous and detailed study of the spectral operator, a map that sends the geometry of fractal strings onto their spectrum. To that effect, they use and develop methods from fractal geometry, functional analysis, complex analysis, operator theory, partial differential equations, analytic number theory and mathematical physics.Originally, M L Lapidus and M van Frankenhuijsen 'heuristically' introduced the spectral operator in their development of the theory of fractal strings and their complex dimensions, specifically in their reinterpretation of the earlier work of M L Lapidus and H Maier on inverse spectral problems for fractal strings and the Riemann hypothesis.One of the main themes of the book is to provide a rigorous framework within which the corresponding question 'Can one hear the shape of a fractal string?' or, equivalently, 'Can one obtain information about the geometry of a fractal string, given its spectrum?' can be further reformulated in terms of the invertibility or the quasi-invertibility of the spectral operator.The infinitesimal shift of the real line is first precisely defined as a differentiation operator on a family of suitably weighted Hilbert spaces of functions on the real line and indexed by a dimensional parameter c. Then, the spectral operator is defined via the functional calculus as a function of the infinitesimal shift. In this manner, it is viewed as a natural 'quantum' analog of the Riemann zeta function. More precisely, within this framework, the spectral operator is defined as the composite map of the Riemann zeta function with the infinitesimal shift, viewed as an unbounded normal operator acting on the above Hilbert space.It is shown that the quasi-invertibility of the spectral operator is intimately connected to the existence of critical zeros of the Riemann zeta function, leading to a new spectral and operator-theoretic reformulation of the Riemann hypothesis. Accordingly, the spectral operator is quasi-invertible for all values of the dimensional parameter c in the critical interval (0,1) (other than in the midfractal case when c =1/2) if and only if the Riemann hypothesis (RH) is true. A related, but seemingly quite different, reformulation of RH, due to the second author and referred to as an 'asymmetric criterion for RH', is also discussed in some detail: namely, the spectral operator is invertible for all values of c in the left-critical interval (0,1/2) if and only if RH is true.These spectral reformulations of RH also led to the discovery of several 'mathematical phase transitions' in this context, for the shape of the spectrum, the invertibility, the boundedness or the unboundedness of the spectral operator, and occurring either in the midfractal case or in the most fractal case when the underlying fractal dimension is equal to ½ or 1, respectively. In particular, the midfractal dimension c=1/2 is playing the role of a critical parameter in quantum statistical physics and the theory of phase transitions and critical phenomena.Furthermore, the authors provide a 'quantum analog' of Voronin's classical theorem about the universality of the Riemann zeta function. Moreover, they obtain and study quantized counterparts of the Dirichlet series and of the Euler product for the Riemann zeta function, which are shown to converge (in a suitable sense) even inside the critical strip.For pedagogical reasons, most of the book is devoted to the study of the quantized Riemann zeta function. However, the results obtained in this monograph are expected to lead to a quantization of most classic arithmetic zeta functions, hence, further 'naturally quantizing' various aspects of analytic number theory and arithmetic geometry.The book should be accessible to experts and non-experts alike, including mathematics and physics graduate students and postdoctoral researchers, interested in fractal geometry, number theory, operator theory and functional analysis, differential equations, complex analysis, spectral theory, as well as mathematical and theoretical physics. Whenever necessary, suitable background about the different subjects involved is provided and the new work is placed in its proper historical context. Several appendices supplementing the main text are also included.

Quantized Number Theory, Fractal Strings And The Riemann Hypothesis: From Spectral Operators To Phase Transitions And Universality

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Author :
Publisher : World Scientific
ISBN 13 : 9813230819
Total Pages : 494 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Quantized Number Theory, Fractal Strings And The Riemann Hypothesis: From Spectral Operators To Phase Transitions And Universality by : Hafedh Herichi

Download or read book Quantized Number Theory, Fractal Strings And The Riemann Hypothesis: From Spectral Operators To Phase Transitions And Universality written by Hafedh Herichi and published by World Scientific. This book was released on 2021-07-27 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studying the relationship between the geometry, arithmetic and spectra of fractals has been a subject of significant interest in contemporary mathematics. This book contributes to the literature on the subject in several different and new ways. In particular, the authors provide a rigorous and detailed study of the spectral operator, a map that sends the geometry of fractal strings onto their spectrum. To that effect, they use and develop methods from fractal geometry, functional analysis, complex analysis, operator theory, partial differential equations, analytic number theory and mathematical physics.Originally, M L Lapidus and M van Frankenhuijsen 'heuristically' introduced the spectral operator in their development of the theory of fractal strings and their complex dimensions, specifically in their reinterpretation of the earlier work of M L Lapidus and H Maier on inverse spectral problems for fractal strings and the Riemann hypothesis.One of the main themes of the book is to provide a rigorous framework within which the corresponding question 'Can one hear the shape of a fractal string?' or, equivalently, 'Can one obtain information about the geometry of a fractal string, given its spectrum?' can be further reformulated in terms of the invertibility or the quasi-invertibility of the spectral operator.The infinitesimal shift of the real line is first precisely defined as a differentiation operator on a family of suitably weighted Hilbert spaces of functions on the real line and indexed by a dimensional parameter c. Then, the spectral operator is defined via the functional calculus as a function of the infinitesimal shift. In this manner, it is viewed as a natural 'quantum' analog of the Riemann zeta function. More precisely, within this framework, the spectral operator is defined as the composite map of the Riemann zeta function with the infinitesimal shift, viewed as an unbounded normal operator acting on the above Hilbert space.It is shown that the quasi-invertibility of the spectral operator is intimately connected to the existence of critical zeros of the Riemann zeta function, leading to a new spectral and operator-theoretic reformulation of the Riemann hypothesis. Accordingly, the spectral operator is quasi-invertible for all values of the dimensional parameter c in the critical interval (0,1) (other than in the midfractal case when c =1/2) if and only if the Riemann hypothesis (RH) is true. A related, but seemingly quite different, reformulation of RH, due to the second author and referred to as an 'asymmetric criterion for RH', is also discussed in some detail: namely, the spectral operator is invertible for all values of c in the left-critical interval (0,1/2) if and only if RH is true.These spectral reformulations of RH also led to the discovery of several 'mathematical phase transitions' in this context, for the shape of the spectrum, the invertibility, the boundedness or the unboundedness of the spectral operator, and occurring either in the midfractal case or in the most fractal case when the underlying fractal dimension is equal to ½ or 1, respectively. In particular, the midfractal dimension c=1/2 is playing the role of a critical parameter in quantum statistical physics and the theory of phase transitions and critical phenomena.Furthermore, the authors provide a 'quantum analog' of Voronin's classical theorem about the universality of the Riemann zeta function. Moreover, they obtain and study quantized counterparts of the Dirichlet series and of the Euler product for the Riemann zeta function, which are shown to converge (in a suitable sense) even inside the critical strip.For pedagogical reasons, most of the book is devoted to the study of the quantized Riemann zeta function. However, the results obtained in this monograph are expected to lead to a quantization of most classic arithmetic zeta functions, hence, further 'naturally quantizing' various aspects of analytic number theory and arithmetic geometry.The book should be accessible to experts and non-experts alike, including mathematics and physics graduate students and postdoctoral researchers, interested in fractal geometry, number theory, operator theory and functional analysis, differential equations, complex analysis, spectral theory, as well as mathematical and theoretical physics. Whenever necessary, suitable background about the different subjects involved is provided and the new work is placed in its proper historical context. Several appendices supplementing the main text are also included.

The Theory of the Riemann Zeta-function

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Author :
Publisher : Oxford University Press
ISBN 13 : 9780198533696
Total Pages : 428 pages
Book Rating : 4.5/5 (336 download)

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Book Synopsis The Theory of the Riemann Zeta-function by : Edward Charles Titchmarsh

Download or read book The Theory of the Riemann Zeta-function written by Edward Charles Titchmarsh and published by Oxford University Press. This book was released on 1986 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Riemann zeta-function is our most important tool in the study of prime numbers, and yet the famous "Riemann hypothesis" at its core remains unsolved. This book studies the theory from every angle and includes new material on recent work.

Spectral Theory of Infinite-Area Hyperbolic Surfaces

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Author :
Publisher : Birkhäuser
ISBN 13 : 3319338773
Total Pages : 471 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Spectral Theory of Infinite-Area Hyperbolic Surfaces by : David Borthwick

Download or read book Spectral Theory of Infinite-Area Hyperbolic Surfaces written by David Borthwick and published by Birkhäuser. This book was released on 2016-07-12 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides a natural setting for development of the spectral theory while still keeping technical difficulties to a minimum. All of the material from the first edition is included and updated, and new sections have been added. Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis of the resolvent of the Laplacian, scattering theory, resonances and scattering poles, the Selberg zeta function, the Poisson formula, distribution of resonances, the inverse scattering problem, Patterson-Sullivan theory, and the dynamical approach to the zeta function. The new sections cover the latest developments in the field, including the spectral gap, resonance asymptotics near the critical line, and sharp geometric constants for resonance bounds. A new chapter introduces recently developed techniques for resonance calculation that illuminate the existing results and conjectures on resonance distribution. The spectral theory of hyperbolic surfaces is a point of intersection for a great variety of areas, including quantum physics, discrete groups, differential geometry, number theory, complex analysis, and ergodic theory. This book will serve as a valuable resource for graduate students and researchers from these and other related fields. Review of the first edition: "The exposition is very clear and thorough, and essentially self-contained; the proofs are detailed...The book gathers together some material which is not always easily available in the literature...To conclude, the book is certainly at a level accessible to graduate students and researchers from a rather large range of fields. Clearly, the reader...would certainly benefit greatly from it." (Colin Guillarmou, Mathematical Reviews, Issue 2008 h)

Selberg Zeta Functions and Transfer Operators

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Author :
Publisher : Springer
ISBN 13 : 331951296X
Total Pages : 363 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Selberg Zeta Functions and Transfer Operators by : Markus Szymon Fraczek

Download or read book Selberg Zeta Functions and Transfer Operators written by Markus Szymon Fraczek and published by Springer. This book was released on 2017-05-11 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters. Studying zeros of Selberg zeta functions for character deformations allows us to access the discrete spectra and resonances of hyperbolic Laplacians under both singular and non-singular perturbations. Areas in which the theory has not yet been sufficiently developed, such as the spectral theory of transfer operators or the singular perturbation theory of hyperbolic Laplacians, will profit from the numerical experiments discussed in this book. Detailed descriptions of numerical approaches to the spectra and eigenfunctions of transfer operators and to computations of Selberg zeta functions will be of value to researchers active in analysis, while those researchers focusing more on numerical aspects will benefit from discussions of the analytic theory, in particular those concerning the transfer operator method and the spectral theory of hyperbolic spaces.

An Introduction to the Theory of the Riemann Zeta-Function

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Author :
Publisher : Cambridge University Press
ISBN 13 : 9780521499057
Total Pages : 176 pages
Book Rating : 4.4/5 (99 download)

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Book Synopsis An Introduction to the Theory of the Riemann Zeta-Function by : S. J. Patterson

Download or read book An Introduction to the Theory of the Riemann Zeta-Function written by S. J. Patterson and published by Cambridge University Press. This book was released on 1995-02-02 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the analytic techniques used in the investigation of zeta functions through the example of the Riemann zeta function. It emphasizes central ideas of broad application, avoiding technical results and the customary function-theoretic appro

Cohomological Theory of Dynamical Zeta Functions

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Author :
Publisher : Birkhäuser
ISBN 13 : 3034883404
Total Pages : 712 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Cohomological Theory of Dynamical Zeta Functions by : Andreas Juhl

Download or read book Cohomological Theory of Dynamical Zeta Functions written by Andreas Juhl and published by Birkhäuser. This book was released on 2012-12-06 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical zeta functions are associated to dynamical systems with a countable set of periodic orbits. The dynamical zeta functions of the geodesic flow of lo cally symmetric spaces of rank one are known also as the generalized Selberg zeta functions. The present book is concerned with these zeta functions from a cohomological point of view. Originally, the Selberg zeta function appeared in the spectral theory of automorphic forms and were suggested by an analogy between Weil's explicit formula for the Riemann zeta function and Selberg's trace formula ([261]). The purpose of the cohomological theory is to understand the analytical properties of the zeta functions on the basis of suitable analogs of the Lefschetz fixed point formula in which periodic orbits of the geodesic flow take the place of fixed points. This approach is parallel to Weil's idea to analyze the zeta functions of pro jective algebraic varieties over finite fields on the basis of suitable versions of the Lefschetz fixed point formula. The Lefschetz formula formalism shows that the divisors of the rational Hassc-Wcil zeta functions are determined by the spectra of Frobenius operators on l-adic cohomology.

Lectures on Mean Values of the Riemann Zeta Function

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Author :
Publisher : Springer Verlag
ISBN 13 : 9783540547488
Total Pages : 0 pages
Book Rating : 4.5/5 (474 download)

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Book Synopsis Lectures on Mean Values of the Riemann Zeta Function by : A. Ivić

Download or read book Lectures on Mean Values of the Riemann Zeta Function written by A. Ivić and published by Springer Verlag. This book was released on 1991 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an advanced text on the Riemann zeta-function, a continuation of theauthor's earlier book. It presents the most recent results on mean values, many of which had not yet appeared in print at the time of the writing of the text. An especially detailed discussion is given of the second and the fourth moment, and the latter is studied by the use of spectral theory, one of the most powerful methods used lately in analytic number theory. The book presupposes a reasonable knowledge of zeta-function theory and complex analysis. It will be of great use to the researchers in the field, an to all those who wish to get well acquainted with the subject or who have the need for application of zeta-function theory.

Exploring the Riemann Zeta Function

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Author :
Publisher : Springer
ISBN 13 : 3319599690
Total Pages : 300 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Exploring the Riemann Zeta Function by : Hugh Montgomery

Download or read book Exploring the Riemann Zeta Function written by Hugh Montgomery and published by Springer. This book was released on 2017-09-11 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects. The book focuses on both old and new results towards the solution of long-standing problems as well as it features some key historical remarks. The purpose of this volume is to present in a unified way broad and deep areas of research in a self-contained manner. It will be particularly useful for graduate courses and seminars as well as it will make an excellent reference tool for graduate students and researchers in Mathematics, Mathematical Physics, Engineering and Cryptography.

Spectral Theory of Automorphic Functions

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 9780821830789
Total Pages : 196 pages
Book Rating : 4.8/5 (37 download)

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Book Synopsis Spectral Theory of Automorphic Functions by : A. B. Venkov

Download or read book Spectral Theory of Automorphic Functions written by A. B. Venkov and published by American Mathematical Soc.. This book was released on 1983 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to the Theory of the Riemann Zeta-Function

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Author :
Publisher : Cambridge University Press
ISBN 13 : 131658335X
Total Pages : 172 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis An Introduction to the Theory of the Riemann Zeta-Function by : S. J. Patterson

Download or read book An Introduction to the Theory of the Riemann Zeta-Function written by S. J. Patterson and published by Cambridge University Press. This book was released on 1995-02-02 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a modern introduction to the analytic techniques used in the investigation of zeta functions, through the example of the Riemann zeta function. Riemann introduced this function in connection with his study of prime numbers and from this has developed the subject of analytic number theory. Since then many other classes of 'zeta function' have been introduced and they are now some of the most intensively studied objects in number theory. Professor Patterson has emphasised central ideas of broad application, avoiding technical results and the customary function-theoretic approach. Thus, graduate students and non-specialists will find this an up-to-date and accessible introduction, especially for the purposes of algebraic number theory. There are many exercises included throughout, designed to encourage active learning.

Analysis IV

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Publisher : Springer
ISBN 13 : 3319169076
Total Pages : 535 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Analysis IV by : Roger Godement

Download or read book Analysis IV written by Roger Godement and published by Springer. This book was released on 2015-04-30 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis Volume IV introduces the reader to functional analysis (integration, Hilbert spaces, harmonic analysis in group theory) and to the methods of the theory of modular functions (theta and L series, elliptic functions, use of the Lie algebra of SL2). As in volumes I to III, the inimitable style of the author is recognizable here too, not only because of his refusal to write in the compact style used nowadays in many textbooks. The first part (Integration), a wise combination of mathematics said to be `modern' and `classical', is universally useful whereas the second part leads the reader towards a very active and specialized field of research, with possibly broad generalizations.