Gauss Sums and the Pólya–Vinogradov Inequality

 

Title: Gauss Sums and the Pólya–Vinogradov Inequality
Authors: Rodrigo Raya and Manuel Eberl
Submission date: 2019-12-10
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
BibTeX:
@article{Gauss_Sums-AFP,
  author  = {Rodrigo Raya and Manuel Eberl},
  title   = {Gauss Sums and the Pólya–Vinogradov Inequality},
  journal = {Archive of Formal Proofs},
  month   = dec,
  year    = 2019,
  note    = {\url{http://isa-afp.org/entries/Gauss_Sums.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License
Depends on: Dirichlet_L, Dirichlet_Series, Polynomial_Interpolation