Analytic Number Theory for Undergraduates

This book is written for undergraduates who wish to learn some basic results in analytic number theory. It covers topics such as Bertrand's Postulate, the Prime Number Theorem and Dirichlet's Theorem of primes in arithmetic progression.

The materials in this book are based on A Hildebrand's 1991 lectures delivered at the University of Illinois at Urbana-Champaign and the author's course conducted at the National University of Singapore from 2001 to 2008.

Contents:

• Facts about Integers
• Arithmetical Functions
• Averages of Arithmetical Functions
• Elementary Results on the Distribution of Primes
• The Prime Number Theorem
• Dirichlet Series
• Primes in Arithmetic Progression

Readership: Final-year undergraduates and first-year graduates with basic knowledge of complex analysis and abstract algebra; academics.
Key Features:

• A textbook on analytic number theory accessible to undergraduates with basic knowledge of complex analysis and abstract algebra
• Prime Number Theorem and Dirichlet's Theorem on primes in arithmetic progression are carefully discussed in this book
• Ramanujan's proof of Bertrand's postulate using Stirling's formula for the gamma function is given