000			03635nam a2200289Ia 4500
003			OSt
005			20240201194253.0
008			231229s9999 xx 000 0 und d
020			_a9781470462857
040			_cIISER BPR
041			_aEng
082			_a512.73 _bKOU _223rd
100			_aKoukoulopoulos, Dimitris
245		0	_aDistribution of prime numbers
250			_a1st ed.
260			_aRhode Island: _bAmerican Mathematical Society, _cc2019.
300			_axii, 356p. : _b(pbk). ; _c24cm.
440			_aGraduate Studies in Mathematics ; _vVol. 203
520			_aPrime numbers have fascinated mathematicians since the time of Euclid. This book presents some of our best tools to capture the properties of these fundamental objects, beginning with the most basic notions of asymptotic estimates and arriving at the forefront of mathematical research. Detailed proofs of the recent spectacular advances on small and large gaps between primes are made accessible for the first time in textbook form. Some other highlights include an introduction to probabilistic methods, a detailed study of sieves, and elements of the theory of pretentious multiplicative functions leading to a proof of Linnik's theorem. Throughout, the emphasis has been placed on explaining the main ideas rather than the most general results available. As a result, several methods are presented in terms of concrete examples that simplify technical details, and theorems are stated in a form that facilitates the understanding of their proof at the cost of sacrificing some generality. Each chapter concludes with numerous exercises of various levels of difficulty aimed to exemplify the material, as well as to expose the readers to more advanced topics and point them to further reading sources. It's clear that Koukoulopoulos had a marvelous time putting together this beautiful material and producing a very readable and pedagogically sound text (replete with good exercises). The book is well-paced and reads very well. The careful reader, with pencil and paper in hand, keen to do exercises galore and have fun doing so, will learn a lot of beautiful number theory and find out marvels about the secret life of the set of primes: they are elusive but not unyielding. --Michael Berg, Loyola Marymount University ...this is an excellent book introducing the reader to a wealth of modern techniques for studying prime numbers. There is a lot of new material here that has never appeared before in book form. The author took great care in explaining both the intuition behind this very technical subject and in providing the 'best' proofs, especially proofs that are short and understandable. The book will be an excellent introduction to anybody interested in primes at a research level (or rather, interested in quickly reaching this level). --Maksym Radziwi, University of Texas at Austin The book under review is a really beautiful guide to the mysteries involving the distribution of prime numbers. The book is written in such a manner to introduce beginning graduate students as well as advanced undergraduate students to the related methods of analytic number theory. A very nice aspect of this work is that the author gives emphasis on demonstrating the main ideas involved, thus making the presentation and flow of the book much more natural and reader friendly. --Michael Th.Rassias (Zürich) Includes list of notations, appendices, bibliography and index.
650			_aMathematics
650			_aNumbers, Prime
650			_aNumber Theory
942			_cBK _2ddc
942			_2ddc
947			_a7409.7395
948			_a22
999			_c3226 _d3226