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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.
"The author has written a monograph with new results in a new direction of research in probability and number theory, including algebraic number theory. ... The book is presented in a clear style and will be valuable for researchers in the field." (Oto Strauch, Mathematical Reviews, October, 2015)
"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 theanswers." (Darren Glass, MAA Reviews, July, 2015)
"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 theanswers." (Darren Glass, MAA Reviews, July, 2015)