L函数加权广义二次高斯和的高阶矩

IF 0.5 4区数学 Q3 MATHEMATICS

Asian Journal of Mathematics Pub Date : 2021-04-20 DOI:10.4310/ajm.2021.v25.n3.a5

Nilanjan Bag, Rupam Barman

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引用次数: 4

摘要

摘要本文的主要目的是利用特征和估计和解析方法研究l函数加权广义二次高斯和的高阶矩。在研究广义二次高斯和的高阶矩时，我们得到了三个特征和的渐近公式。然后，我们使用这些特征和估计来找到由l函数加权的广义二次高斯和的6阶和8阶矩的渐近公式。我们的渐近公式满足张文鹏的一个猜想。

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Higher order moments of generalized quadratic Gauss sums weighted by $L$-functions

Abstract. The main purpose of this paper is to study higher order moments of the generalized quadratic Gauss sums weighted by L-functions using estimates for character sums and analytic methods. We find asymptotic formulas for three character sums which arise naturally in the study of higher order moments of the generalized quadratic Gauss sums. We then use these character sum estimates to find asymptotic formulas for the 6 and 8 order moments of the generalized quadratic Gauss sums weighted by L-functions. Our asymptotic formulas satisfy a conjecture of Wenpeng Zhang.

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