### 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

### License

BSD License

### Topics

- Mathematics/Number theory

### Session Gauss_Sums

- Gauss_Sums_Auxiliary
- Periodic_Arithmetic
- Complex_Roots_Of_Unity
- Finite_Fourier_Series
- Ramanujan_Sums
- Gauss_Sums
- Polya_Vinogradov

### Depends on

- Dirichlet L-Functions and Dirichlet’s Theorem
- Dirichlet Series
- Polynomial Interpolation

### Auto-related entries

- Elementary Facts About the Distribution of Primes

## Cite

×

Gauss_Sums-AFP

    @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{https://isa-afp.org/entries/Gauss_Sums.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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