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arXiv · 2104.09888

An explicit evaluation of $\nth{10}$-power moment of quadratic Gauss sums and some applications

Nilanjan Bag·Antonio Rojas-León·Zhang Wenpeng
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Abstract

In this paper we have estimated one multi-variable character sum \begin{align*} \sum_{a=2}^{p-2}\sum_{b=1}^{p-1}\sum_{c=2}^{p-2}\sum_{d=1}^{p-1}\left(\frac{a^2-b^2}{p}\right)\left(\frac{b^2-1}{p}\right) \left(\frac{c^2-d^2}{p}\right)\left(\frac{d^2-1}{p}\right)\left(\frac{a^2c^2-1}{p}\right), \end{align*} for odd prime $p$. With the help of our estimate of the above character sum, we have studied the tenth power mean value of generalized quadratic Gauss sums using estimates for character sums and analytic methods.

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Nilanjan Bag, Antonio Rojas-León, Zhang Wenpeng. 2021-04-20. An explicit evaluation of $\nth{10}$-power moment of quadratic Gauss sums and some applications. https://arxiv.org/abs/2104.09888

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