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Probabilistic Diophantine Approximation [electronic resource] : Randomness in Lattice Point Counting / by József Beck

Author
Beck, József
Published
Cham : Springer International Publishing : Imprint: Springer, 2014.
Physical Description
XVI, 487 pages 22 illustrations : online resource
Additional Creators
SpringerLink (Online service)
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Contents
Preface.- 1 What is "probabilistic" diophantine approximation?.- 2 Expectation, and its connection with quadratic fields.- 3 Variance, and its connection with quadratic fields.- 4 Proving randomness.- 5 Pell equation, super irregularity and randomness.- 6 More on randomness -- References -- Index.
Summary
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.
Subject(s)
ISBN
9783319107417
Digital File Characteristics
text file PDF
Note
AVAILABLE ONLINE TO AUTHORIZED PSU USERS.
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Springer eBooks
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