Topics in Analytic Number Theory

Topics in Analytic Number Theory is a comprehensive book written by Serge Lang, a renowned mathematician, that covers a wide range of topics in the field of analytic number theory. The book is divided into five parts and includes 18 chapters, each of which provides a detailed explanation of a specific topic in the field.Part I of the book covers the basic principles of analytic number theory, including the Riemann zeta function, prime numbers, and the distribution of primes. Part II delves deeper into the theory of the Riemann zeta function and its applications, including the prime number theorem and the Riemann hypothesis.Part III of the book focuses on modular forms and their applications in number theory, including the theory of elliptic curves and the Langlands program. Part IV covers topics related to automorphic forms and their connections to number theory, including the Selberg trace formula and the theory of L-functions.Finally, Part V of the book explores various topics related to algebraic number theory, including the theory of number fields, class field theory, and the Brauer-Siegel theorem.Overall, Topics in Analytic Number Theory is a highly informative and comprehensive book that provides a thorough introduction to the field of analytic number theory. It is an essential resource for mathematicians and researchers studying number theory, as well as advanced students looking to deepen their understanding of this fascinating subject.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.