Probabilistic Diophantine Approximation: Randomness in Lattice Point Counting by József Beck
English | PDF(Repost),EPUB | 2014 | 497 Pages | ISBN : 3319107402 | 12.54 MB
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.