Introduction to Analytic Number Theory

Tom M. Apostol

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English

Springer Verlag
01 July 1998

Mathematics & Sciences; Number theory

Series: Undergraduate Texts in Mathematics

This introductory textbook is designed to teach undergraduates the basic ideas and techniques of number theory, with special consideration to the principles of analytic number theory. The first five chapters treat elementary concepts such as divisibility, congruence and arithmetical functions. The topics in the next chapters include Dirichlet's theorem on primes in progressions, Gauss sums, quadratic residues, Dirichlet series, and Euler products with applications to the Riemann zeta function and Dirichlet L-functions. Also included is an introduction to partitions. Among the strong points of the book are its clarity of exposition and a collection of exercises at the end of each chapter. The first ten chapters, with the exception of one section, are accessible to anyone with knowledge of elementary calculus; the last four chapters require some knowledge of complex function theory including complex integration and residue calculus.

By: Tom M. Apostol
Imprint: Springer Verlag
Country of Publication: United States
Edition: 5th
Dimensions: Height: 235mm, Width: 155mm, Spine: 20mm
Weight: 699g
ISBN: 9780387901633
ISBN 10: 0387901639
Series: Undergraduate Texts in Mathematics
Pages: 338
Publication Date: 01 July 1998
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Historical Introduction.- 1 The Fundamental Theorem of Arithmetic.- 2 Arithmetical Functions and Dirichlet Multiplication.- 3 Averages of Arithmetical Functions.- 4 Some Elementary Theorems on the Distribution of Prime Numbers.- 5 Congruences.- 6 Finite Abelian Groups and Their Characters.- 7 Dirichlet’s Theorem on Primes in Arithmetic Progressions.- 8 Periodic Arithmetical Functions and Gauss Sums.- 9 Quadratic Residues and the Quadratic Reciprocity Law.- 10 Primitive Roots.- 11 Dirichlet Series and Euler Products.- 12 The Functions ?(s) and L(s, ?).- 13 Analytic Proof of the Prime Number Theorem.- 14 Partitions.- Index of Special Symbols.

Reviews for Introduction to Analytic Number Theory

"T.M. Apostol Introduction to Analytic Number Theory ""This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages. The presentation is invariably lucid and the book is a real pleasure to read."" -MATHEMATICAL REVIEWS"