The Prime Number Theorem

ISBN-13: 9780521814119 / Angielski / Twarda / 2003 / 264 str.

Graham Jameson; G. J. O. Jameson; C. M. Series

Opis

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.

Recenzje

'The book is engagingly written, in a friendly style, and there are short biographies of the mathematicians most associated with the prime number theorem. Given the complexity and depth of the mathematics needed, I doubt that a more accessible account of the theorem exists.' The Mathematical Gazette

Spis treści

Preface; 1. Foundations; 2. Some important Dirichlet series and arithmetic functions; 3. The basic theorems; 4. Prime numbers in residue classes: Dirichlet's theorem; 5. Error estimates and the Riemann hypothesis; 6. An 'elementary' proof of the prime number theorem; Appendices; Bibliography; Index.