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arXiv · 2207.12439

Equidistribution and independence of Gauss sums

Antonio Rojas-León
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Abstract

We prove a general independent equidistribution result for Gauss sums associated to $n$ monomials in $r$ variable multiplicative characters over a finite field, which generalizes several previous equidistribution results for Gauss and Jacobi sums. As an application, we show that any relation satisfied by these Gauss sums must be a combination of the conjugation relation $G(χ)G(\overlineχ)=\pm q$, Galois conjugation invariance and the Hasse-Davenport product formula.

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Antonio Rojas-León. 2024-05-13. Equidistribution and independence of Gauss sums. https://arxiv.org/abs/2207.12439

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