Problems in Analytic Number Theory

M. Ram Murty (auth.)0387723498, 9780387723495

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

Table of contents :
Front Matter….Pages i-xxi
Arithmetic Functions….Pages 3-15
Primes in Arithmetic Progressions….Pages 17-33
The Prime Number Theorem….Pages 35-51
The Method of Contour Integration….Pages 53-68
Functional Equations….Pages 69-83
Hadamard Products….Pages 85-99
Explicit Formulas….Pages 101-113
The Selberg Class….Pages 115-126
Sieve Methods….Pages 127-146
p -adic Methods….Pages 147-170
Equidistribution….Pages 171-195
Arithmetic Functions….Pages 199-236
Primes in Arithmetic Progressions….Pages 237-271
The Prime Number Theorem….Pages 273-304
The Method of Contour Integration….Pages 305-328
Functional Equations….Pages 329-356
Hadamard Products….Pages 357-383
Explicit Formulas….Pages 385-402
The Selberg Class….Pages 403-421
Sieve Methods….Pages 423-447
p -adic Methods….Pages 449-473
Equidistribution….Pages 475-496
Back Matter….Pages 497-502