Introduction to Analytic Number Theory

  • Tom M. Apostol
Book

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xii
    PDF
  2. Historical Introduction
    Tom M. Apostol
    Pages 1-12
  3. The Fundamental Theorem of Arithmetic
    Tom M. Apostol
    Pages 13-23
  4. Arithmetical Functions and Dirichlet Multiplication
    Tom M. Apostol
    Pages 24-51
  5. Averages of Arithmetical Functions
    Tom M. Apostol
    Pages 52-73
  6. Some Elementary Theorems on the Distribution of Prime Numbers
    Tom M. Apostol
    Pages 74-105
  7. Congruences
    Tom M. Apostol
    Pages 106-128
  8. Finite Abelian Groups and Their Characters
    Tom M. Apostol
    Pages 129-145
  9. Dirichlet’s Theorem on Primes in Arithmetical Progressions
    Tom M. Apostol
    Pages 146-156
  10. Periodic Arithmetical Functions and Gauss Sums
    Tom M. Apostol
    Pages 157-177
  11. Quadratic Residues and the Quadratic Reciprocity Law
    Tom M. Apostol
    Pages 178-203
  12. Primitive Roots
    Tom M. Apostol
    Pages 204-223
  13. Dirichlet Series and Euler Products
    Tom M. Apostol
    Pages 224-248
  14. The Functions ζ(s) and L(s, χ)
    Tom M. Apostol
    Pages 249-277
  15. Analytic Proof of the Prime Number Theorem
    Tom M. Apostol
    Pages 278-303
  16. Partitions
    Tom M. Apostol
    Pages 304-328
  17. Back Matter
    Pages 329-340
    PDF

About this book

Keywords

Analytische Zahlentheorie Prime Prime number Riemann zeta function calculus number theory

Authors and affiliations

  • Tom M. Apostol
    • 1
  1. 1.Department of MathematicsCalifornia Institute of TechnologyPasadenaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-5579-4
  • Copyright Information Springer-Verlag New York 1976
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2805-4
  • Online ISBN 978-1-4757-5579-4
  • Series Print ISSN 0172-6056
  • About this book