The prime number theorem / G.J.O. Jameson.

Includes bibliographical references (pages 249-250) and index.

Print version record.

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 us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material.

1. Foundations -- 2. Some important Dirichlet series and arithmetic functions -- 3. basic theorems -- 4. Prime numbers in residue classes: Dirichlet's theorem -- 5. Error estimates and the Riemann hypothesis -- 6. "elementary" proof of the prime number theorem -- App. A. Complex functions of a real variable -- App. B. Double series and multiplication of series -- App. C. Infinite products -- App. D. Differentiation under the integral sign -- App. E. O, o notation -- App. F. Computing values of [pi](x) -- App. G. Table of primes -- App. H. Biographical notes.

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