{"product_id":"9783319107400","title":"Probabilistic Diophantine Approximation : Randomness in Lattice Point Counting (Springer Monographs in Mathematics)","description":"\u003cp\u003eThis 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 \u003ci\u003eL\u003c\/i\u003e-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.\u003c\/p\u003e\u003cp\u003eWritten by one of the acknowledged experts in the field, \u003ci\u003eProbabilistic Diophantine Approximation\u003c\/i\u003e is presented in a clear and informal style with sufficient detail to appeal to both advanced students and researchers in number theory.\u003c\/p\u003e 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.\u003cbr\u003e József Beck is Harold H. Martin Professor of Mathematics at Rutgers University. \u003cp\u003e\"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)\u003c\/p\u003e\u003cp\u003e\"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)\u003c\/p\u003e\u003cp\u003e\"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)\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Default Title","offer_id":49178884538595,"sku":"00000_00000_00000_00000","price":109.99,"currency_code":"USD","in_stock":true}],"url":"https:\/\/usa.kinokuniya.com\/products\/9783319107400","provider":"Books Kinokuniya USA","version":"1.0","type":"link"}