Probabilistic Diophantine Approximation
Randomness in Lattice Point Counting
Authors: Beck, Jozsef
Free Preview- Includes many insights into diophantine approximation by one of the field's leading contributors
- Covers both classical results and recent research developments
- Provides detailed and well-motivated proofs, enabling the reader to grasp key ideas behind difficult arguments
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- About this book
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This book gives a comprehensive treatment of random phenomena and distribution results in diophantine approximation, with a particular emphasis on quadratic irrationals. It covers classical material on the subject as well as many new results developed by the author over the past decade. A range of ideas from other areas of mathematics are brought to bear with surprising connections to topics such as formulae for class numbers, special values of L-functions, and Dedekind sums. Care is taken to elaborate difficult proofs by motivating major steps and accompanying them with background explanations, enabling the reader to learn the theory and relevant techniques.
Written by one of the acknowledged experts in the field, Probabilistic Diophantine Approximation is presented in a clear and informal style with sufficient detail to appeal to both advanced students and researchers in number theory.
- About the authors
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József Beck is Harold H. Martin Professor of Mathematics at Rutgers University.
- Reviews
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“The author has written a monograph with new results in a new direction of research in probability and number theory, including algebraic number theory. … The book is presented in a clear style and will be valuable for researchers in the field.” (Oto Strauch, Mathematical Reviews, October, 2015)
“Novel, important, intuitively appealing mathematics and a highly readable account. Summing Up: Highly recommended. Upper-division undergraduates and above.” (D. V. Feldman, Choice, Vol. 52 (11), July, 2015)
“Beck’s book brings together probability theory, algebraic number theory, and combinatorics to forge new ground. … the book is accessible to a wide range of mathematicians. … Beck did a nice job of motivating the questions and explaining the answers.” (Darren Glass, MAA Reviews, July, 2015)
- Table of contents (6 chapters)
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What Is “Probabilistic” Diophantine Approximation?
Pages 3-78
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Expectation, and Its Connection with Quadratic Fields
Pages 79-165
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Variance, and Its Connection with Quadratic Fields
Pages 167-206
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Proving Randomness
Pages 207-247
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Pell’s Equation, Superirregularity and Randomness
Pages 251-369
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Table of contents (6 chapters)
- Download Preface 1 PDF (92.7 KB)
- Download Sample pages 1 PDF (840.4 KB)
- Download Table of contents PDF (43.8 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Probabilistic Diophantine Approximation
- Book Subtitle
- Randomness in Lattice Point Counting
- Authors
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- Jozsef Beck
- Series Title
- Springer Monographs in Mathematics
- Copyright
- 2014
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing Switzerland
- eBook ISBN
- 978-3-319-10741-7
- DOI
- 10.1007/978-3-319-10741-7
- Hardcover ISBN
- 978-3-319-10740-0
- Softcover ISBN
- 978-3-319-35465-1
- Series ISSN
- 1439-7382
- Edition Number
- 1
- Number of Pages
- XVI, 487
- Number of Illustrations
- 22 b/w illustrations
- Topics
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