Probabilistic Diophantine Approximation

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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

Zusammenfassung

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

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2014
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Springer Monographs in Mathematics
Inhalt:	xvi 487 S. 22 s/w Illustr. 487 p. 22 illus.
ISBN-13:	9783319107400
ISBN-10:	3319107402
Sprache:	Englisch
Herstellernummer:	86339370
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Beck, József
Hersteller:	Springer International Publishing Springer International Publishing AG Springer Monographs in Mathematics
Maße:	241 x 160 x 33 mm
Von/Mit:	József Beck
Erscheinungsdatum:	22.10.2014
Gewicht:	0,916 kg

Artikel-ID: 105178219