03329nam 22006255 450 991029996620332120200703235356.03-319-10741-010.1007/978-3-319-10741-7(CKB)3710000000251908(EBL)1963383(OCoLC)893674008(SSID)ssj0001372749(PQKBManifestationID)11761814(PQKBTitleCode)TC0001372749(PQKBWorkID)11310804(PQKB)11282022(MiAaPQ)EBC1963383(DE-He213)978-3-319-10741-7(PPN)182098567(EXLCZ)99371000000025190820141004d2014 u| 0engur|n|---|||||txtccrProbabilistic Diophantine Approximation Randomness in Lattice Point Counting /by József Beck1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (497 p.)Springer Monographs in Mathematics,1439-7382Description based upon print version of record.3-319-10740-2 Includes bibliographical references and index.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.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.Springer Monographs in Mathematics,1439-7382Number theoryProbabilitiesNumber Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Number theory.Probabilities.Number Theory.Probability Theory and Stochastic Processes.512.73Beck Józsefauthttp://id.loc.gov/vocabulary/relators/aut348406MiAaPQMiAaPQMiAaPQBOOK9910299966203321Probabilistic diophantine approximation1409953UNINA