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
Author(s): Tom M. Apostol
Series: Undergraduate Texts in Mathematics
Publisher: Springer
Year: 2010
Language: English
Pages: C+xii, 338
Front Matter
Pages i-xii
Book Chapter
Pages 1-12
Historical Introduction
Book Chapter
Pages 13-23
The Fundamental Theorem of Arithmetic
Book Chapter
Pages 24-51
Arithmetical Functions and Dirichlet Multiplication
Book Chapter
Pages 52-73
Averages of Arithmetical Functions
Book Chapter
Pages 74-105
Some Elementary Theorems on the Distribution of Prime Numbers
Book Chapter
Pages 106-128
Congruences
Book Chapter
Pages 129-145
Finite Abelian Groups and Their Characters
Book Chapter
Pages 146-156
Dirichlet's Theorem on Primes in Arithmetical Progressions
Book Chapter
Pages 157-177
Periodic Arithmetical Functions and Gauss Sums
Book Chapter
Pages 178-203
Quadratic Residues and the Quadratic Reciprocity Law
Book Chapter
Pages 204-223
Primitive Roots
Book Chapter
Pages 224-248
Dirichlet Series and Euler Products
Book Chapter
Pages 249-277
The Functions ζ(s) and L(s, χ)
Book Chapter
Pages 278-303
Analytic Proof of the Prime Number Theorem
Book Chapter
Pages 304-328
Partitions
Back Matter
Pages 329-340
