Springer Monographs in Mathematics

Probabilistic Diophantine Approximation

Randomness in Lattice Point Counting

Authors: Beck, Jozsef

  • 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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eBook 79,72 €
price for Spain (gross)
  • ISBN 978-3-319-10741-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 98,79 €
price for Spain (gross)
  • ISBN 978-3-319-10740-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 98,79 €
price for Spain (gross)
  • ISBN 978-3-319-35465-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

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

József Beck is Harold H. Martin Professor of Mathematics at Rutgers University.

Reviews

“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)

  • What Is “Probabilistic” Diophantine Approximation?

    Beck, József

    Pages 3-78

    Preview Buy Chapter 30,19 €
  • Expectation, and Its Connection with Quadratic Fields

    Beck, József

    Pages 79-165

    Preview Buy Chapter 30,19 €
  • Variance, and Its Connection with Quadratic Fields

    Beck, József

    Pages 167-206

    Preview Buy Chapter 30,19 €
  • Proving Randomness

    Beck, József

    Pages 207-247

    Preview Buy Chapter 30,19 €
  • Pell’s Equation, Superirregularity and Randomness

    Beck, József

    Pages 251-369

    Preview Buy Chapter 30,19 €

Buy this book

eBook 79,72 €
price for Spain (gross)
  • ISBN 978-3-319-10741-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 98,79 €
price for Spain (gross)
  • ISBN 978-3-319-10740-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 98,79 €
price for Spain (gross)
  • ISBN 978-3-319-35465-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Probabilistic Diophantine Approximation
Book Subtitle
Randomness in Lattice Point Counting
Authors
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 and Tables
22 b/w illustrations
Topics