Introduction to Analytic Number Theory

ISBN-10: 0387901639
ISBN-13: 9780387901633
Edition: 1976
Authors: Tom M. Apostol
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Description: 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  More...

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Book details

List price: $69.95
Copyright year: 1976
Publisher: Springer
Publication date: 5/28/1998
Binding: Hardcover
Pages: 340
Size: 6.50" wide x 9.75" long x 1.00" tall
Weight: 1.628
Language: English

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.

Tom Apostol is an Emeritus Professor of Mathematics at the California Institute of Technology.

The Fundamental Theorem of Arithmetic
Arithmetical Functions and Dirichlet Multiplication
Averages of Arithmetical Function
Some Elementary Theorems on the Distribution of Prime Numbers
Congruences
Finite Abelian Groups and Their Characters
Cirichlet's Theorem on Primes in Arithmetic Progressions
Periodic Arithmetical Functions and Gauss Sums
Quadratic Residues and the Quadratic Reciprocity Law
Primitive Roots
Dirichlet Series and Euler Products
The Functions
Analytic Proof of the Prime Number Theorem
Partitions

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