TY  - BOOK
AU  - Beck,Jozsef
TI  - Probabilistic diophantine approximation : : randomness in lattice point counting 
T2  - Springer monographs in mathematics
SN  - 9783319107400
U1  - 512.73 23
PY  - 2014///
CY  - Switzerland : 
PB  - Springer
KW  - Diophantine approximation
N1  - Includes bibliographical references and index; 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's equation, superirregularity and randomness --
 6. More on randomness
N2  - 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.
ER  -