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The Prime Number Theorem de Graham Jameson

The Prime Number Theorem

Autor Graham Jameson, G. J. O. Jameson Editat de C. M. Series
en Limba Engleză Hardback – 31 aug 2007
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.
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Specificații

ISBN-13: 9780521814119
ISBN-10: 0521814111
Pagini: 264
Ilustrații: 1 b/w illus.
Dimensiuni: 157 x 235 x 20 mm
Greutate: 0.58 kg
Editura: Cambridge University Press
Locul publicării:New York, United States

Cuprins

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.

Recenzii

'The entire exposition is extremely lucid, motivated and amply commentated throughout. With numerous examples illustrating the purely theoretical parts. Unquestionably, the book bespeaks the author's teaching skill and experience just as much as his gripping passion for this refined and fascinating topic. Altogether, this textbook is outstandingly suitable for both a course on prime number theory, at the upper-graduate level, and as a source for self-instruction … Anyway, this text is a highly valuable enhancement of the existing literature on the subject which stands out by its particular user-friendliness.' Zentralblatt MATH
'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

Descriere

This textbook demonstrates how the tools of analysis can be used in number theory to attack a famous problem.