Gauss sum

Summary

A Gauss sum is a finite sum $\sum_a \chi(a)\psi(a)$ over a finite field, where $\chi$ is a multiplicative character and $\psi$ an additive character. It mixes the multiplicative and the additive structure of the field. Its absolute value is the square root of the field size when both characters are nontrivial. Gauss sums are a basic tool in proofs of reciprocity laws and in the study of character sums and Dirichlet L-functions.