Number Theory, Trace Formulas and Discrete Groups

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Publisher : Academic Press
ISBN 13 : 1483216233
Total Pages : 537 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Number Theory, Trace Formulas and Discrete Groups by : Karl Egil Aubert

Download or read book Number Theory, Trace Formulas and Discrete Groups written by Karl Egil Aubert and published by Academic Press. This book was released on 2014-05-10 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number Theory, Trace Formulas and Discrete Groups: Symposium in Honor of Atle Selberg Oslo, Norway, July 14-21, 1987 is a collection of papers presented at the 1987 Selberg Symposium, held at the University of Oslo. This symposium contains 30 lectures that cover the significant contribution of Atle Selberg in the field of mathematics. This book is organized into three parts encompassing 29 chapters. The first part presents a brief introduction to the history and developments of the zeta-function. The second part contains lectures on Selberg's considerable research studies on understanding the principles of several aspects of mathematics, including in modular forms, the Riemann zeta function, analytic number theory, sieve methods, discrete groups, and trace formula. The third part is devoted to Selberg's further research works on these topics, with particular emphasis on their practical applications. Some of these research studies, including the integral representations of Einstein series and L-functions; first eigenvalue for congruence groups; the zeta function of a Kleinian group; and the Waring's problem are discussed. This book will prove useful to mathematicians, researchers, and students.

Representation Theory and Automorphic Forms

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Publisher : American Mathematical Soc.
ISBN 13 : 0821806092
Total Pages : 490 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Representation Theory and Automorphic Forms by : T. N. Bailey

Download or read book Representation Theory and Automorphic Forms written by T. N. Bailey and published by American Mathematical Soc.. This book was released on 1997 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lectures from a course in the representation theory of semi- simple groups, automorphic forms, and the relations between them. The purpose is to help analysts make systematic use of Lie groups in work on harmonic analysis, differential equations, and mathematical physics; and to provide number theorists with the representation-theoretic input to Wiles's proof of Fermat's Last Theorem. Begins with an introductory treatment of structure theory and ends with the current status of functionality. Annotation copyrighted by Book News, Inc., Portland, OR

Fourier Analysis on Finite Groups and Applications

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Publisher : Cambridge University Press
ISBN 13 : 9780521457187
Total Pages : 456 pages
Book Rating : 4.4/5 (571 download)

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Book Synopsis Fourier Analysis on Finite Groups and Applications by : Audrey Terras

Download or read book Fourier Analysis on Finite Groups and Applications written by Audrey Terras and published by Cambridge University Press. This book was released on 1999-03-28 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: It examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research.

Advanced Analytic Number Theory: L-Functions

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Publisher : American Mathematical Soc.
ISBN 13 : 0821842668
Total Pages : 313 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Advanced Analytic Number Theory: L-Functions by : Carlos J. Moreno

Download or read book Advanced Analytic Number Theory: L-Functions written by Carlos J. Moreno and published by American Mathematical Soc.. This book was released on 2005 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois representations. This book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and non-vanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of Artin-Hecke and automorphic L-functions is also given. The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of L-functions and their applications in number theory and in the theory of automorphic representations. The requirements for a profitable study of this monograph are a knowledge of basic number theory and the rudiments of abstract harmonic analysis on locally compact abelian groups.

Emerging Applications of Number Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 1461215447
Total Pages : 693 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Emerging Applications of Number Theory by : Dennis A. Hejhal

Download or read book Emerging Applications of Number Theory written by Dennis A. Hejhal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging - providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern number-theoretical techniques.

Dynamics, Geometry, Number Theory

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Publisher : University of Chicago Press
ISBN 13 : 022680402X
Total Pages : 573 pages
Book Rating : 4.2/5 (268 download)

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Book Synopsis Dynamics, Geometry, Number Theory by : David Fisher

Download or read book Dynamics, Geometry, Number Theory written by David Fisher and published by University of Chicago Press. This book was released on 2022-02-07 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mathematicians David Fisher, Dmitry Kleinbock, and Gregory Soifer highlight in this edited collection the foundations and evolution of research by mathematician Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics. Margulis' ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani. The broad goal of this volume is to introduce these areas, their development, their use in current research, and the connections between them. The foremost experts on the topic have written each of the chapters in this volume with a view to making them accessible by graduate students and by experts in other parts of mathematics"--

The Heat Kernel and Theta Inversion on SL2(C)

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Publisher : Springer Science & Business Media
ISBN 13 : 0387380329
Total Pages : 314 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis The Heat Kernel and Theta Inversion on SL2(C) by : Jay Jorgenson

Download or read book The Heat Kernel and Theta Inversion on SL2(C) written by Jay Jorgenson and published by Springer Science & Business Media. This book was released on 2009-02-20 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: The worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2,Z[i])\SL(2,C). Unlike other treatments of the theory, the approach taken here is to begin with the heat kernel on SL(2,C) associated to the invariant Laplacian, which is derived using spherical inversion. The heat kernel on the quotient space SL(2,Z[i])\SL(2,C) is arrived at through periodization, and further expanded in an eigenfunction expansion. A theta inversion formula is obtained by studying the trace of the heat kernel. Following the author's previous work, the inversion formula then leads to zeta functions through the Gauss transform./

Harmonic Analysis on Symmetric Spaces—Higher Rank Spaces, Positive Definite Matrix Space and Generalizations

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Publisher : Springer
ISBN 13 : 1493934082
Total Pages : 500 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Harmonic Analysis on Symmetric Spaces—Higher Rank Spaces, Positive Definite Matrix Space and Generalizations by : Audrey Terras

Download or read book Harmonic Analysis on Symmetric Spaces—Higher Rank Spaces, Positive Definite Matrix Space and Generalizations written by Audrey Terras and published by Springer. This book was released on 2016-04-26 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an introduction to harmonic analysis on symmetric spaces, focusing on advanced topics such as higher rank spaces, positive definite matrix space and generalizations. It is intended for beginning graduate students in mathematics or researchers in physics or engineering. As with the introductory book entitled "Harmonic Analysis on Symmetric Spaces - Euclidean Space, the Sphere, and the Poincaré Upper Half Plane, the style is informal with an emphasis on motivation, concrete examples, history, and applications. The symmetric spaces considered here are quotients X=G/K, where G is a non-compact real Lie group, such as the general linear group GL(n,P) of all n x n non-singular real matrices, and K=O(n), the maximal compact subgroup of orthogonal matrices. Other examples are Siegel's upper half "plane" and the quaternionic upper half "plane". In the case of the general linear group, one can identify X with the space Pn of n x n positive definite symmetric matrices. Many corrections and updates have been incorporated in this new edition. Updates include discussions of random matrix theory and quantum chaos, as well as recent research on modular forms and their corresponding L-functions in higher rank. Many applications have been added, such as the solution of the heat equation on Pn, the central limit theorem of Donald St. P. Richards for Pn, results on densest lattice packing of spheres in Euclidean space, and GL(n)-analogs of the Weyl law for eigenvalues of the Laplacian in plane domains. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, fundamental domains in X for discrete groups Γ (such as the modular group GL(n,Z) of n x n matrices with integer entries and determinant ±1), connections with the problem of finding densest lattice packings of spheres in Euclidean space, automorphic forms, Hecke operators, L-functions, and the Selberg trace formula and its applications in spectral theory as well as number theory.

Surveys in Noncommutative Geometry

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821838464
Total Pages : 212 pages
Book Rating : 4.8/5 (384 download)

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Book Synopsis Surveys in Noncommutative Geometry by : Nigel Higson

Download or read book Surveys in Noncommutative Geometry written by Nigel Higson and published by American Mathematical Soc.. This book was released on 2006 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: In June 2000, the Clay Mathematics Institute organized an Instructional Symposium on Noncommutative Geometry in conjunction with the AMS-IMS-SIAM Joint Summer Research Conference. These events were held at Mount Holyoke College in Massachusetts from June 18 to 29, 2000. The Instructional Symposium consisted of several series of expository lectures which were intended to introduce key topics in noncommutative geometry to mathematicians unfamiliar with the subject. Those expository lectures have been edited and are reproduced in this volume. The lectures of Rosenberg and Weinberger discuss various applications of noncommutative geometry to problems in ``ordinary'' geometry and topology. The lectures of Lagarias and Tretkoff discuss the Riemann hypothesis and the possible application of the methods of noncommutative geometry in number theory. Higson gives an account of the ``residue index theorem'' of Connes and Moscovici. Noncommutative geometry is to an unusual extent the creation of a single mathematician, Alain Connes. The present volume gives an extended introduction to several aspects of Connes' work in this fascinating area. Information for our distributors: Titles in this series are copublished with the Clay Mathematics Institute (Cambridge, MA).

Rational Number Theory in the 20th Century

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Publisher : Springer Science & Business Media
ISBN 13 : 0857295322
Total Pages : 659 pages
Book Rating : 4.8/5 (572 download)

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Book Synopsis Rational Number Theory in the 20th Century by : Władysław Narkiewicz

Download or read book Rational Number Theory in the 20th Century written by Władysław Narkiewicz and published by Springer Science & Business Media. This book was released on 2011-09-02 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.

Number Theory and Modular Forms

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Publisher : Springer Science & Business Media
ISBN 13 : 1475760442
Total Pages : 392 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Number Theory and Modular Forms by : Bruce C. Berndt

Download or read book Number Theory and Modular Forms written by Bruce C. Berndt and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robert A. Rankin, one of the world's foremost authorities on modular forms and a founding editor of The Ramanujan Journal, died on January 27, 2001, at the age of 85. Rankin had broad interests and contributed fundamental papers in a wide variety of areas within number theory, geometry, analysis, and algebra. To commemorate Rankin's life and work, the editors have collected together 25 papers by several eminent mathematicians reflecting Rankin's extensive range of interests within number theory. Many of these papers reflect Rankin's primary focus in modular forms. It is the editors' fervent hope that mathematicians will be stimulated by these papers and gain a greater appreciation for Rankin's contributions to mathematics. This volume would be an inspiration to students and researchers in the areas of number theory and modular forms.

Smooth Ergodic Theory and Its Applications

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Publisher : American Mathematical Soc.
ISBN 13 : 0821826824
Total Pages : 895 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Smooth Ergodic Theory and Its Applications by : A. B. Katok

Download or read book Smooth Ergodic Theory and Its Applications written by A. B. Katok and published by American Mathematical Soc.. This book was released on 2001 with total page 895 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past decade, there have been several major new developments in smooth ergodic theory, which have attracted substantial interest to the field from mathematicians as well as scientists using dynamics in their work. In spite of the impressive literature, it has been extremely difficult for a student-or even an established mathematician who is not an expert in the area-to acquire a working knowledge of smooth ergodic theory and to learn how to use its tools. Accordingly, the AMS Summer Research Institute on Smooth Ergodic Theory and Its Applications (Seattle, WA) had a strong educational component, including ten mini-courses on various aspects of the topic that were presented by leading experts in the field. This volume presents the proceedings of that conference. Smooth ergodic theory studies the statistical properties of differentiable dynamical systems, whose origin traces back to the seminal works of Poincare and later, many great mathematicians who made contributions to the development of the theory. The main topic of this volume, smooth ergodic theory, especially the theory of nonuniformly hyperbolic systems, provides the principle paradigm for the rigorous study of complicated or chaotic behavior in deterministic systems. This paradigm asserts that if a non-linear dynamical system exhibits sufficiently pronounced exponential behavior, then global properties of the system can be deduced from studying the linearized system. One can then obtain detailed information on topological properties (such as the growth of periodic orbits, topological entropy, and dimension of invariant sets including attractors), as well as statistical properties (such as the existence of invariant measures, asymptotic behavior of typical orbits, ergodicity, mixing, decay of corre This volume serves a two-fold purpose: first, it gives a useful gateway to smooth ergodic theory for students and nonspecialists, and second, it provides a state-of-the-art report on important current aspects of the subject. The book is divided into three parts: lecture notes consisting of three long expositions with proofs aimed to serve as a comprehensive and self-contained introduction to a particular area of smooth ergodic theory; thematic sections based on mini-courses or surveys held at the conference; and original contributions presented at the meeting or closely related to the topics that were discussed there.

A Pythagorean Introduction to Number Theory

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Publisher : Springer
ISBN 13 : 3030026043
Total Pages : 279 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis A Pythagorean Introduction to Number Theory by : Ramin Takloo-Bighash

Download or read book A Pythagorean Introduction to Number Theory written by Ramin Takloo-Bighash and published by Springer. This book was released on 2018-11-26 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Right triangles are at the heart of this textbook’s vibrant new approach to elementary number theory. Inspired by the familiar Pythagorean theorem, the author invites the reader to ask natural arithmetic questions about right triangles, then proceeds to develop the theory needed to respond. Throughout, students are encouraged to engage with the material by posing questions, working through exercises, using technology, and learning about the broader context in which ideas developed. Progressing from the fundamentals of number theory through to Gauss sums and quadratic reciprocity, the first part of this text presents an innovative first course in elementary number theory. The advanced topics that follow, such as counting lattice points and the four squares theorem, offer a variety of options for extension, or a higher-level course; the breadth and modularity of the later material is ideal for creating a senior capstone course. Numerous exercises are included throughout, many of which are designed for SageMath. By involving students in the active process of inquiry and investigation, this textbook imbues the foundations of number theory with insights into the lively mathematical process that continues to advance the field today. Experience writing proofs is the only formal prerequisite for the book, while a background in basic real analysis will enrich the reader’s appreciation of the final chapters.

Number Theory

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Publisher : Birkhäuser
ISBN 13 : 303487023X
Total Pages : 525 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Number Theory by : R.P. Bambah

Download or read book Number Theory written by R.P. Bambah and published by Birkhäuser. This book was released on 2012-12-06 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Indian National Science Academy on the occasion ofthe Golden Jubilee Celebration (Fifty years of India's Independence) decided to publish a number of monographs on the selected fields. The editorial board of INS A invited us to prepare a special monograph in Number Theory. In reponse to this assignment, we invited several eminent Number Theorists to contribute expository/research articles for this monograph on Number Theory. Al though some ofthose invited, due to other preoccupations-could not respond positively to our invitation, we did receive fairly encouraging response from many eminent and creative number theorists throughout the world. These articles are presented herewith in a logical order. We are grateful to all those mathematicians who have sent us their articles. We hope that this monograph will have a significant impact on further development in this subject. R. P. Bambah v. C. Dumir R. J. Hans-Gill A Centennial History of the Prime Number Theorem Tom M. Apostol The Prime Number Theorem Among the thousands of discoveries made by mathematicians over the centuries, some stand out as significant landmarks. One of these is the prime number theorem, which describes the asymptotic distribution of prime numbers. It can be stated in various equivalent forms, two of which are: x (I) K(X) '" -I - as x --+ 00, ogx and Pn '" n log n as n --+ 00. (2) In (1), K(X) denotes the number of primes P ::s x for any x > O.

Number Theory

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821873274
Total Pages : 430 pages
Book Rating : 4.8/5 (732 download)

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Book Synopsis Number Theory by : Canadian Number Theory Association. Conference

Download or read book Number Theory written by Canadian Number Theory Association. Conference and published by American Mathematical Soc.. This book was released on 1999-01-01 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers presented at the fifth Canadian Number Theory Association (CNTA) conference held at Carleton University (Ottawa, ON). The invited speakers focused on arithmetic algebraic geometry and elliptic curves, diophantine problems, analytic number theory, and algebraic and computational number theory. The contributed talks represented a wide variety of areas in number theory. David Boyd gave an hour-long talk on "Mahler's Measure and Elliptic Curves". This lecture was open to the public and attracted a large audience from outside the conference.

The Mysteries of the Real Prime

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Publisher : Oxford University Press
ISBN 13 : 9780198508687
Total Pages : 262 pages
Book Rating : 4.5/5 (86 download)

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Book Synopsis The Mysteries of the Real Prime by : M. J. Shai Haran

Download or read book The Mysteries of the Real Prime written by M. J. Shai Haran and published by Oxford University Press. This book was released on 2001 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Highly topical and original monograph, introducing the author's work on the Riemann zeta function and its adelic interpretation of interest to a wide range of mathematicians and physicists.

Some Musings on Theta, Eta, and Zeta

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Author :
Publisher : Springer Nature
ISBN 13 : 9819953367
Total Pages : 233 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis Some Musings on Theta, Eta, and Zeta by : Floyd L. Williams

Download or read book Some Musings on Theta, Eta, and Zeta written by Floyd L. Williams and published by Springer Nature. This book was released on with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: