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Chapter 27. Functions of Number Theory

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Acknowledgments:
The author thanks Basil Gordon for comments on an earlier draft, and David Bressoud for providing §§27.12, 27.18, 27.19, and 27.22.
Referenced by:
Tom M. Apostol, Tab.1
Permalink:
http://dlmf.nist.gov/27
T. M. Apostol
California Institute of Technology, Pasadena, CA.
Thumbnail imagePrime Number Theorem
  • Notation
    • §27.1 Special Notation
  • Multiplicative Number Theory
    • §27.2 Functions
    • §27.3 Multiplicative Properties
    • §27.4 Euler Products and Dirichlet Series
    • §27.5 Inversion Formulas
    • §27.6 Divisor Sums
    • §27.7 Lambert Series as Generating Functions
    • §27.8 Dirichlet Characters
    • §27.9 Quadratic Characters
    • §27.10 Periodic Number-Theoretic Functions
    • §27.11 Asymptotic Formulas: Partial Sums
    • §27.12 Asymptotic Formulas: Primes
  • Additive Number Theory
    • §27.13 Functions
    • §27.14 Unrestricted Partitions
  • Applications
    • §27.15 Chinese Remainder Theorem
    • §27.16 Cryptography
    • §27.17 Other Applications
  • Computation
    • §27.18 Methods of Computation: Primes
    • §27.19 Methods of Computation: Factorization
    • §27.20 Methods of Computation: Other Number-Theoretic Functions
    • §27.21 Tables
    • §27.22 Software
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