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

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
  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{},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License
Depends on: Dirichlet_L, Dirichlet_Series, Polynomial_Interpolation
Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.