Continued Fractions From Analytic Number Theory To Constructive Approximation

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Continued Fractions

Author : Leo Jerome Lange
Publisher : American Mathematical Soc.
ISBN 13 : 9780821855720
Total Pages : 404 pages
Book Rating : 4.8/5 (557 download)

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Book Synopsis Continued Fractions by : Leo Jerome Lange

Download or read book Continued Fractions written by Leo Jerome Lange and published by American Mathematical Soc.. This book was released on 1999-07-28 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the contributions from the international conference held at the University of Missouri at Columbia, marking Professor Lange's 70th birthday and his retirement from the university. The principal purpose of the conference was to focus on continued fractions as a common interdisciplinary theme bridging gaps between a large number of fields--from pure mathematics to mathematical physics and approximation theory. Evident in this work is the widespread influence of continued fractions in a broad range of areas of mathematics and physics, including number theory, elliptic functions, Pade approximations, orthogonal polynomials, moment problems, frequency analysis, and regularity properties of evolution equations. Different areas of current research are represented. The lectures at the conference and the contributions to this volume reflect the wide range of applicability of continued fractions in mathematics and the applied sciences.

Continued Fractions: From Analytic Number Theory to Constructive Approximation

Author : Bruce C. Berndt
Publisher : American Mathematical Soc.
ISBN 13 : 0821812009
Total Pages : 402 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Continued Fractions: From Analytic Number Theory to Constructive Approximation by : Bruce C. Berndt

Download or read book Continued Fractions: From Analytic Number Theory to Constructive Approximation written by Bruce C. Berndt and published by American Mathematical Soc.. This book was released on 1999 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the contributions from the international conference held at the University of Missouri at Columbia, marking Professor Lange's 70th birthday and his retirement from the university. The principal purpose of the conference was to focus on continued fractions as a common interdisciplinary theme bridging gaps between a large number of fields-from pure mathematics to mathematical physics and approximation theory. Evident in this work is the widespread influence of continued fractions in a broad range of areas of mathematics and physics, including number theory, elliptic functions, Padé approximations, orthogonal polynomials, moment problems, frequency analysis, and regularity properties of evolution equations. Different areas of current research are represented. The lectures at the conference and the contributions to this volume reflect the wide range of applicability of continued fractions in mathematics and the applied sciences.

Continued Fractions

Author : Bruce Carl Berndt (Mathematiker, USA)
Publisher :
ISBN 13 : 9780821878279
Total Pages : 0 pages
Book Rating : 4.8/5 (782 download)

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Book Synopsis Continued Fractions by : Bruce Carl Berndt (Mathematiker, USA)

Download or read book Continued Fractions written by Bruce Carl Berndt (Mathematiker, USA) and published by . This book was released on 1999 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Continued Fractions From Analytic Number Theory to Constructive Approximation

Author : Bruce C. Berndt
Publisher :
ISBN 13 :
Total Pages : 402 pages
Book Rating : 4.:/5 (827 download)

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Book Synopsis Continued Fractions From Analytic Number Theory to Constructive Approximation by : Bruce C. Berndt

Download or read book Continued Fractions From Analytic Number Theory to Constructive Approximation written by Bruce C. Berndt and published by . This book was released on 1999 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analytic Theory of Continued Fractions

Author : Hubert Stanley Wall
Publisher : Courier Dover Publications
ISBN 13 : 0486823695
Total Pages : 449 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Analytic Theory of Continued Fractions by : Hubert Stanley Wall

Download or read book Analytic Theory of Continued Fractions written by Hubert Stanley Wall and published by Courier Dover Publications. This book was released on 2018-05-16 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most authoritative and comprehensive books on continued fractions, this monograph presents a unified theory correlating certain parts and applications of the subject within a larger analytic structure. 1948 edition.

Continued Fractions

Author : Aleksandr I?Akovlevich Khinchin
Publisher : Courier Corporation
ISBN 13 : 0486696308
Total Pages : 114 pages
Book Rating : 4.4/5 (866 download)

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Book Synopsis Continued Fractions by : Aleksandr I?Akovlevich Khinchin

Download or read book Continued Fractions written by Aleksandr I?Akovlevich Khinchin and published by Courier Corporation. This book was released on 1997-05-14 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions. Clear, straightforward presentation of the properties of the apparatus, the representation of numbers by continued fractions, and the measure theory of continued fractions. 1964 edition. Prefaces.

Continued Fractions

Author : Doug Hensley
Publisher : World Scientific
ISBN 13 : 9814479438
Total Pages : 261 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Continued Fractions by : Doug Hensley

Download or read book Continued Fractions written by Doug Hensley and published by World Scientific. This book was released on 2006-03-01 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Euclidean algorithm is one of the oldest in mathematics, while the study of continued fractions as tools of approximation goes back at least to Euler and Legendre. While our understanding of continued fractions and related methods for simultaneous diophantine approximation has burgeoned over the course of the past decade and more, many of the results have not been brought together in book form. Continued fractions have been studied from the perspective of number theory, complex analysis, ergodic theory, dynamic processes, analysis of algorithms, and even theoretical physics, which has further complicated the situation.This book places special emphasis on continued fraction Cantor sets and the Hausdorff dimension, algorithms and analysis of algorithms, and multi-dimensional algorithms for simultaneous diophantine approximation. Extensive, attractive computer-generated graphics are presented, and the underlying algorithms are discussed and made available.

Analytic And Combinatorial Number Theory: The Legacy Of Ramanujan - Contributions In Honor Of Bruce C. Berndt

Author : George E Andrews
Publisher : World Scientific
ISBN 13 : 9811277389
Total Pages : 704 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Analytic And Combinatorial Number Theory: The Legacy Of Ramanujan - Contributions In Honor Of Bruce C. Berndt by : George E Andrews

Download or read book Analytic And Combinatorial Number Theory: The Legacy Of Ramanujan - Contributions In Honor Of Bruce C. Berndt written by George E Andrews and published by World Scientific. This book was released on 2024-08-19 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reflects the contributions stemming from the conference Analytic and Combinatorial Number Theory: The Legacy of Ramanujan which took place at the University of Illinois at Urbana-Champaign on June 6-9, 2019. The conference included 26 plenary talks, 71 contributed talks, and 170 participants. As was the case for the conference, this book is in honor of Bruce C Berndt and in celebration of his mathematics and his 80th birthday.Along with a number of papers previously appearing in Special Issues of the International Journal of Number Theory, the book collects together a few more papers, a biography of Bruce by Atul Dixit and Ae Ja Yee, a preface by George Andrews, a gallery of photos from the conference, a number of speeches from the conference banquet, the conference poster, a list of Bruce's publications at the time this volume was created, and a list of the talks from the conference.

Continued Fractions

Author : A. M. Rockett
Publisher : World Scientific
ISBN 13 : 9789810210526
Total Pages : 202 pages
Book Rating : 4.2/5 (15 download)

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Book Synopsis Continued Fractions by : A. M. Rockett

Download or read book Continued Fractions written by A. M. Rockett and published by World Scientific. This book was released on 1992-08-01 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the arithmetic and metrical theory of regular continued fractions and is intended to be a modern version of A. Ya. Khintchine's classic of the same title. Besides new and simpler proofs for many of the standard topics, numerous numerical examples and applications are included (the continued fraction of e, Ostrowski representations and t-expansions, period lengths of quadratic surds, the general Pell's equation, homogeneous and inhomogeneous diophantine approximation, Hall's theorem, the Lagrange and Markov spectra, asymmetric approximation, etc). Suitable for upper level undergraduate and beginning graduate students, the presentation is self-contained and the metrical results are developed as strong laws of large numbers.

Ramanujan's Lost Notebook

Author : George E. Andrews
Publisher : Springer Science & Business Media
ISBN 13 : 038728124X
Total Pages : 438 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Ramanujan's Lost Notebook by : George E. Andrews

Download or read book Ramanujan's Lost Notebook written by George E. Andrews and published by Springer Science & Business Media. This book was released on 2005-12-06 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the library at Trinity College, Cambridge in 1976, George Andrews of Pennsylvania State University discovered a sheaf of pages in the handwriting of Srinivasa Ramanujan. Soon designated as "Ramanujan’s Lost Notebook," it contains considerable material on mock theta functions and undoubtedly dates from the last year of Ramanujan’s life. In this book, the notebook is presented with additional material and expert commentary.

Geometry of Continued Fractions

Author : Oleg Karpenkov
Publisher : Springer Science & Business Media
ISBN 13 : 3642393683
Total Pages : 409 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Geometry of Continued Fractions by : Oleg Karpenkov

Download or read book Geometry of Continued Fractions written by Oleg Karpenkov and published by Springer Science & Business Media. This book was released on 2013-08-15 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.

Number Theory and Related Fields

Author : Jonathan M. Borwein
Publisher : Springer Science & Business Media
ISBN 13 : 1461466423
Total Pages : 395 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Number Theory and Related Fields by : Jonathan M. Borwein

Download or read book Number Theory and Related Fields written by Jonathan M. Borwein and published by Springer Science & Business Media. This book was released on 2013-05-16 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Number Theory and Related Fields” collects contributions based on the proceedings of the "International Number Theory Conference in Memory of Alf van der Poorten," hosted by CARMA and held March 12-16th 2012 at the University of Newcastle, Australia. The purpose of the conference was to promote number theory research in Australia while commemorating the legacy of Alf van der Poorten, who had written over 170 papers on the topic of number theory and collaborated with dozens of researchers. The research articles and surveys presented in this book were written by some of the most distinguished mathematicians in the field of number theory, and articles will include related topics that focus on the various research interests of Dr. van der Poorten.

Arithmetic and Geometry

Author : Gisbert Wüstholz
Publisher : Princeton University Press
ISBN 13 : 0691193789
Total Pages : 186 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Arithmetic and Geometry by : Gisbert Wüstholz

Download or read book Arithmetic and Geometry written by Gisbert Wüstholz and published by Princeton University Press. This book was released on 2019-10-08 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Lectures by outstanding scholars on progress made in the past ten years in the most progressive areas of arithmetic and geometry - primarily arithmetic geometry"--

Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis

Author : Eric Grinberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821811487
Total Pages : 524 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis by : Eric Grinberg

Download or read book Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis written by Eric Grinberg and published by American Mathematical Soc.. This book was released on 2000 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings from the conference honoring the work of Leon Ehrenpreis. Professor Ehrenpreis worked in many different areas of mathematics and found connections among all of them. For example, one can find his analytic ideas in the context of number theory, geometric thinking within analysis, transcendental number theory applied to partial differential equations, and more. The conference brought together the communities of mathematicians working in the areas of interest to Professor Ehrenpreis and allowed them to share the research inspired by his work. The collection of articles here presents current research on PDEs, several complex variables, analytic number theory, integral geometry, and tomography. The work of Professor Ehrenpreis has contributed to basic definitions in these areas and has motivated a wealth of research results. This volume offers a survey of the fundamental principles that unified the conference and influenced the mathematics of Leon Ehrenpreis.

Number Theory and Discrete Mathematics

Author : A.K. Agarwal
Publisher : Birkhäuser
ISBN 13 : 3034882238
Total Pages : 314 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Number Theory and Discrete Mathematics by : A.K. Agarwal

Download or read book Number Theory and Discrete Mathematics written by A.K. Agarwal and published by Birkhäuser. This book was released on 2012-12-06 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: To mark the World Mathematical Year 2000 an International Conference on Number Theory and Discrete Mathematics in honour of the legendary Indian Mathematician Srinivasa Ramanuj~ was held at the centre for Advanced study in Mathematics, Panjab University, Chandigarh, India during October 2-6, 2000. This volume contains the proceedings of that conference. In all there were 82 participants including 14 overseas participants from Austria, France, Hungary, Italy, Japan, Korea, Singapore and the USA. The conference was inaugurated by Prof. K. N. Pathak, Hon. Vice-Chancellor, Panjab University, Chandigarh on October 2, 2000. Prof. Bruce C. Berndt of the University of Illinois, Urbana Chaimpaign, USA delivered the key note address entitled "The Life, Notebooks and Mathematical Contributions of Srinivasa Ramanujan". He described Ramanujan--as one of this century's most influential Mathematicians. Quoting Mark K. ac, Prof. George E. Andrews of the Pennsylvania State University, USA, in his message for the conference, described Ramanujan as a "magical genius". During the 5-day deliberations invited speakers gave talks on various topics in number theory and discrete mathematics. We mention here a few of them just as a sampling: • M. Waldschmidt, in his article, provides a very nice introduction to the topic of multiple poly logarithms and their special values. • C.

Coimbra Lecture Notes on Orthogonal Polynomials

Author : Amilcar Jose Pinto Lopes Branquinho
Publisher : Nova Publishers
ISBN 13 : 9781600219726
Total Pages : 250 pages
Book Rating : 4.2/5 (197 download)

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Book Synopsis Coimbra Lecture Notes on Orthogonal Polynomials by : Amilcar Jose Pinto Lopes Branquinho

Download or read book Coimbra Lecture Notes on Orthogonal Polynomials written by Amilcar Jose Pinto Lopes Branquinho and published by Nova Publishers. This book was released on 2008 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orthogonal Polynomials and Special Functions (OPSF) have a very rich history, going back to 19th century when mathematicians and physicists tried to solve the most important deferential equations of mathematical physics. Hermite-Padé approximation was also introduced at that time, to prove the transcendence of the remarkable constant e (the basis of the natural logarithm). Since then OPSF has developed to a standard subject within mathematics, which is driven by applications. The applications are numerous, both within mathematics (e.g. statistics, combinatory, harmonic analysis, number theory) and other sciences, such as physics, biology, computer science, chemistry. The main reason for the fact that OPSF has been so successful over the centuries is its usefulness in other branches of mathematics and physics, as well as other sciences. There are many different aspects of OPSF. Some of the most important developments for OPSF are related to the theory of rational approximation of analytic functions, in particular the extension to simultaneous rational approximation to a system of functions. Important tools for rational approximation are Riemann-Hilbert problems, the theory of orthogonal polynomials, logarithmic potential theory, and operator theory for difference operators. This new book presents the latest research in the field.

Noise, Oscillators and Algebraic Randomness

Author : Michel Planat
Publisher : Springer
ISBN 13 : 3540454632
Total Pages : 417 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Noise, Oscillators and Algebraic Randomness by : Michel Planat

Download or read book Noise, Oscillators and Algebraic Randomness written by Michel Planat and published by Springer. This book was released on 2008-01-11 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noise is ubiquitous in nature and in man-made systems. Noise in oscillators perturbs high-technology devices such as time standards or digital communication systems. The understanding of its algebraic structure is thus of vital importance. The book addresses both the measurement methods and the understanding of quantum, 1/f and phase noise in systems such as electronic amplifiers, oscillators and receivers, trapped ions, cosmic ray showers and in commercial applications. A strong link between 1/f noise and number theory is emphasized. The twenty papers in the book are comprehensive versions of talks presented at a school in Chapelle des Bois (Jura, France) held from April 6 to 10, 1999, by engineers, physisicts and mathematicians.