The Prime Number Theorem / Edition 1

The Prime Number Theorem / Edition 1

by G. J. O. Jameson
     
 

ISBN-10: 0521891108

ISBN-13: 9780521891103

Pub. Date: 04/28/2007

Publisher: Cambridge University Press

At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells (in an approximate but well-defined sense) how many primes can be found that are less than any integer. The prime number theorem tells what this formula is and it is indisputably one of the the great…  See more details below

Overview

At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells (in an approximate but well-defined sense) how many primes can be found that are less than any integer. The prime number theorem tells what this formula is and it is indisputably one of the the great classical theorems of mathematics. This textbook introduces the prime number theorem and is suitable for advanced undergraduates and beginning graduate students. The author deftly shows how analytical tools can be used in number theory to attack a 'real' problem.

Product Details

ISBN-13:
9780521891103
Publisher:
Cambridge University Press
Publication date:
04/28/2007
Series:
London Mathematical Society Student Texts Series, #53
Edition description:
New Edition
Pages:
264
Product dimensions:
5.98(w) x 8.98(h) x 0.59(d)

Table of Contents

Preface
1Foundations1
2Some important Dirichlet series and arithmetic functions56
3The basic theorems98
4Prime numbers in residue classes: Dirichlet's theorem147
5Error estimates and the Riemann hypothesis178
6An "elementary" proof of the prime number theorem206
App. AComplex functions of a real variable223
App. BDouble series and multiplication of series225
App. CInfinite products228
App. DDifferentiation under the integral sign230
App. EThe O,o notation232
App. FComputing values of [pi](x)234
App. GTable of primes238
App. HBiographical notes240
Bibliography249
Index251

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