List questions from gauss-sums

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quadratic gauss sum calculation in sage

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Show that $S^p = \sum\limits_{x \in \Bbb {F_q}^*} \left ( \frac x q \right ) {\omega}^{xp}.$

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List Question

Gauss sum in regular 7-gon

a special problem about numbers assigned on polygons

Why did people constructed Quadratic Gauss Sum?

Gauss sum possible typo

On a $\mathbb C$-linear map from $M(p-1,\mathbb C)$ to $\mathbb C^\hat G$, where $p$ is an odd prime and $G=\mathbb Z/(p) ^\times$

$\lim_{n\to\infty}\frac{\sum_{i=1}^ni^{4\lambda}}{\Big(\sum_{i=1}^ni^{2\lambda}\Big)^2}=0$

Computing number of solutions for equations in $F_{m^s}$ (finite field with $m^s$ elements)

Jacobi sums Gaussian Sum. Show $J(\rho^{'},\chi^{'}) = (- J(\rho,\chi))^s$

quadratic gauss sum calculation in sage

Show that $S^p = \sum\limits_{x \in \Bbb {F_q}^*} \left ( \frac x q \right ) {\omega}^{xp}.$

What is the reason for taking $\omega$ to be a primitive $q$-th root unity rather than taking any $q$-th root of unity?

Expected maximum of sub-Gaussian

About sums similar to gauss sums

Norm of Gauss Sum = p

Quadratic Fields and Gauss Sums

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