Product 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 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.

Product Details

• Amazon Sales Rank: #39601 in Books
• Published on: 1998-07-01
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 352 pages

Customer Reviews

Postgraduate text assumes you know Complex Analysis
This book claims to be aimed at undergraduates but is really a postgraduate text since it assumes you already know Complex Analysis. Having said that the book is otherwise self-contained for example there is a useful introduction to Abelian Groups where these are required. No advance knowledge of number theory is assumed and the book contains an excellent exposition of Arithmetical Functions and Direchlet Multiplication, Periodic Arithmetical Functions and Gauss sums, Direchlet Series and Euler Products, culminating in an analytic proof of the Prime Number Theorem.

Intro to No. Theory (Apostol)
This is an OU set text for MSC level No. Theory. The book provides an excellent presentation of the subject. Its claim to accessibility by 'sophisticated' high school students is something of a stretch. This post-grad student finds the 'theorem - proof' repetition style rather terse for independent study. I have found 'Jones and Jones, Ele. No. Theory' an indispensible accompaniment. The ubiquitous use of proof by induction can be hard to follow as his style in its use seems to be all his own.

Indispensable
From experience, this book is ideal for an undergraduate module in analytic number theory. Of course it requires knowledge of complex analysis and very basic number theory, but that is the nature of the subject and the way that most books cover it. The foundations such as Dirichlet Series and Euler Products are particularly well covered, while the Prime Number Theorem is discussed towards the end. Most topics in the more analytic side of analytic number theorem appear somewhere in the text. This book can't be beaten (except possibly by the legendary J.-P. Serre...)