A Primer of Analytic Number Theory

Jeffrey Stopple

ISBN 10: 0521012538 / ISBN 13: 9780521012539

Published by Cambridge University Press, GB, 2003

About this Item

This 2003 undergraduate introduction to analytic number theory develops analytic skills in the course of studying ancient questions on polygonal numbers, perfect numbers and amicable pairs. The question of how the primes are distributed amongst all the integers is central in analytic number theory. This distribution is determined by the Riemann zeta function, and Riemann's work shows how it is connected to the zeroes of his function, and the significance of the Riemann Hypothesis. Starting from a traditional calculus course and assuming no complex analysis, the author develops the basic ideas of elementary number theory. The text is supplemented by series of exercises to further develop the concepts, and includes brief sketches of more advanced ideas, to present contemporary research problems at a level suitable for undergraduates. In addition to proofs, both rigorous and heuristic, the book includes extensive graphics and tables to make analytic concepts as concrete as possible.

Seller Inventory # LU-9780521012539

Bibliographic Details

• Title: A Primer of Analytic Number Theory
• Publisher: Cambridge University Press, GB
• Publication Date: 2003
• Language: English
• ISBN 10: 0521012538
• ISBN 13: 9780521012539
• Binding: Paperback
• Condition: New
• Weight: 500 grams

About this title

Synopsis

This undergraduate-level introduction describes those mathematical properties of prime numbers that can be deduced with the tools of calculus. Jeffrey Stopple pays special attention to the rich history of the subject and ancient questions on polygonal numbers, perfect numbers and amicable pairs, as well as to the important open problems. The culmination of the book is a brief presentation of the Riemann zeta function, which determines the distribution of prime numbers, and of the significance of the Riemann Hypothesis.

Book Description

This undergraduate-level introduction describes those mathematical properties of prime numbers that can be deduced with the tools of calculus. The author pays special attention to the rich history of the subject and ancient questions on polygonal numbers, perfect numbers and amicable pairs, as well as to the important open problems (some of which have million dollar prizes). The capstone of the book is a brief presentation of the Riemann zeta function, which determines the distribution of prime numbers, and of the significance of the Riemann Hypothesis.