Probabilistic Diophantine Approximation

Randomness in Lattice Point Counting

Gebonden Engels 2014 2014e druk 9783319107400
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Samenvatting

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.

Specificaties

ISBN13:9783319107400
Taal:Engels
Bindwijze:gebonden
Aantal pagina's:487
Uitgever:Springer International Publishing
Druk:2014

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Inhoudsopgave

<p>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.</p>

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€ 120,99
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        Probabilistic Diophantine Approximation