
Probabilistic Diophantine Approximation
Randomness in Lattice Point Counting
Jozsef Beck(Author)
Springer (Publisher)
Published on 22. October 2014
Book
Hardback
XVI, 487 pages
978-3-319-10740-0 (ISBN)
Description
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.
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.
Reviews / Votes
"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)More details
Product info
Book
Series
Language
English
Place of publication
Cham
Switzerland
Target group
Research
Illustrations
22 s/w Abbildungen
22 schwarz-weiße Abbildungen, Bibliographie
Dimensions
Height: 241 mm
Width: 164 mm
Thickness: 32 mm
Weight
886 gr
ISBN-13
978-3-319-10740-0 (9783319107400)
DOI
10.1007/978-3-319-10741-7
Schweitzer Classification
Other editions
Additional editions

Book
09/2016
Springer
€106.99
Shipment within 10-15 days

E-Book
10/2014
1st Edition
Springer
€96.29
Available for download
Person
József Beck is Harold H. Martin Professor of Mathematics at Rutgers University.
Content
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.