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
Author(s): M. Ram Murty (auth.)
Series: Graduate Texts in Mathematics 206
Edition: 2
Publisher: Springer-Verlag New York
Year: 2008
Language: English
Pages: 506
City: New York
Tags: Number Theory; Combinatorics
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
