Gauss Sums and the Pólya–Vinogradov Inequality

Rodrigo Raya and Manuel Eberl

10 December 2019

Abstract

This article provides a full formalisation of Chapter 8 of Apostol's Introduction to Analytic Number Theory. Subjects that are covered are:

  • periodic arithmetic functions and their finite Fourier series
  • (generalised) Ramanujan sums
  • Gauss sums and separable characters
  • induced moduli and primitive characters
  • the Pólya—Vinogradov inequality
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@article{Gauss_Sums-AFP,
  author  = {Rodrigo Raya and Manuel Eberl},
  title   = {Gauss Sums and the Pólya–Vinogradov Inequality},
  journal = {Archive of Formal Proofs},
  month   = December,
  year    = 2019,
  note    = {\url{http://isa-afp.org/entries/Gauss_Sums.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
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