Probabilistic Diophantine Approximation

Randomness in Lattice Point Counting

  • József Beck

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Global Aspects Randomness of the Irrational Rotation

    1. Front Matter
      Pages 1-1
    2. József Beck
      Pages 207-247
  3. Local Aspects Inhomogeneous Pell Inequalities

    1. Front Matter
      Pages 249-249
    2. József Beck
      Pages 371-479
  4. Back Matter
    Pages 481-487

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.


Markov chains Riesz product area principle inhomogeneous Pell inequalities probabilistic Diophantine approximation quadratic irrational rotation

Authors and affiliations

  • József Beck
    • 1
  1. 1.Department of MathematicsRutgers UniversityPiscatawayUSA

Bibliographic information

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