Explicit Evaluation of Double Gauss Sums

Şaban Alaca; Greg Doyle

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arXiv · 1609.03919

Explicit Evaluation of Double Gauss Sums

Şaban Alaca·Greg Doyle

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Abstract

We present an explicit evaluation of the double Gauss sum $\displaystyle G(a,b,c;S;p^n):=\sum_{x,y=0}^{p^n-1} e^{2\pi i S(ax^2+bxy+cy^2)/p^n}$, where $a, b, c$ are integers such that $\gcd(a,b,c)=1$, $p$ is a prime, $n$ is a positive integer, and $S$ is an integer coprime to $p$.

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Şaban Alaca, Greg Doyle. 2016-09-13. Explicit Evaluation of Double Gauss Sums. https://arxiv.org/abs/1609.03919

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