Problems in Analytic Number Theory

This book is a collection of about 500 problems in analytic number theory with the singular purpose of training the beginning graduate student in some of its significant techniques. This book, along with Murty's other book "Problems in Algebraic Number Theory" are intended to enable the student to gain a quick initiation into the beautiful subject of number theory. Since the subject is rapidly expanding such an expedient route becomes indispensable. The material in these two books provides a "basic tool kit" for the number theorist.

Contains a combination of well-organized theory and problems The problems successfully guide students through the most important areas of analytic number theory Includes more than 500 exercises at varying levels of difficulty Covers an improved Eratosthenes sieve, without the typical combinatorics Includes a clear exposition of Brun's and Selberg's sieves Includes supplementary material: sn.pub/extras

Klappentext

This book gives a problem-solving approach to the difficult subject of analytic number theory. It is primarily aimed at graduate students and senior undergraduates. The goal is to provide a rapid introduction to analytic methods and the ways in which they are used to study the distribution of prime numbers. The book also includes an introduction to p-adic analytic methods. It is ideal for a first course in analytic number theory. The new edition has been completely rewritten, errors have been corrected, and there is a new chapter on equidistribution.

About the first edition:

"...this monograph gives important results and techniques for specific topics, together with many exercises; it is not possible to describe adequately the wealth of material covered in this book."

• Wolfgang Schwarz, Zentralblatt

  Zusammenfassung
  This informative and exhaustive study gives a problem-solving approach to the difficult subject of analytic number theory. It provides a rapid introduction to analytic methods and the ways in which they are used to study the distribution of prime numbers.

  Inhalt
  Problems.- Arithmetic Functions.- Primes in Arithmetic Progressions.- The Prime Number Theorem.- The Method of Contour Integration.- Functional Equations.- Hadamard Products.- Explicit Formulas.- The Selberg Class.- Sieve Methods.- p-adic Methods.- Equidistribution.- Solutions.- Arithmetic Functions.- Primes in Arithmetic Progressions.- The Prime Number Theorem.- The Method of Contour Integration.- Functional Equations.- Hadamard Products.- Explicit Formulas.- The Selberg Class.- Sieve Methods.- p-adic Methods.- Equidistribution.