A primer of analytic number theory : from Pythagoras to Riemann / Jeffrey Stopple.

Format:

Book

Author/Creator:

Stopple, Jeffrey, 1958- author.

Language:

English

Subjects (All):

Number theory.

Physical Description:

1 online resource (xiii, 383 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2003.

Language Note:

English

Summary:

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.

Contents:

Cover; Half-title; Title; Copyright; Dedication; Contents; Preface; Chapter 1 Sums and Differences; Chapter 2 Products and Divisibility; Chapter 3 Order of Magnitude; Chapter 4 Averages; Interlude 1 Calculus; Chapter 5 Primes; Interlude 2 Series; Chapter 6 Basel Problem; Chapter 7 Euler's Product; Interlude 3 Complex Numbers; Chapter 8 The Riemann Zeta Function; Chapter 9 Symmetry; Chapter 10 Explicit Formula; Interlude 4 Modular Arithmetic; Chapter 11 Pell's Equation; Chapter 12 Elliptic Curves; Chapter 13 Analytic Theory of Algebraic Numbers; Solutions; Bibliography; Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 375-377) and index.

ISBN:

1-107-13316-5

1-280-41969-5

9786610419692

0-511-20475-2

0-511-06470-5

0-511-18059-4

0-511-75513-9

0-511-30758-6

0-511-07316-X

OCLC:

171136401