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. 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.

Table of Contents

Chapter I The Fundamental Theorem of Arithmetic

Chapter 2 Arithmetical Functions and Dirichlet Multiplication

Chapter 3 Averages of Arithmetical Functions

Chapter 4 Some Elementary Theorems on the Distribution of Prime Numbers

Chapter 5 Congruences

Chapter 6 Finite Abelian Groups and Their Characters

Chapter 7 Dirichlet's Theorem on Primes in Arithmetic Progressions

Chapter 8 Periodic Arithmetical Functions and Gauss Sums

Chapter 9 Quadratic Residues and the Quadratic Reciprocity Law

Chapter 10 Primitive Roots

Chapter 11 Dirichlet Series and Euler Products

Chapter 12 The Functions ((s) and L(s, x)

Chapter 13 Analytic Proof of the Prime Number Theorem

Chapter 14 Partitions

About the Author

Tom Mike Apostol was an American mathematician and professor at the California Institute of Technology specializing in analytic number theory, best known as the author of widely used mathematical textbooks, including Calculus in two volumes.