关于两类特征和的递推性质

Two kinds of character sums and their recurrence properties

摘要

利用解析的方法、广义 Gauss 和的性质,在模素数 p 的条件下,得到两类特征和 A _k(p)和 T _k(p)的递推公式,本文结果用于解决对角同余方程解的个数问题。

Abstract

Methods of analytic number theory, together with the properties of generalized Gauss sums modulo p are used to derive some third order recurrence formulas involving character sums A _k(p) and T _k(p) under certain conditions for an odd prime p. These results can be applied to solving problems regarding the number of solutions to the general diagonal equation.

关键词

特征和 / 广义 Gauss 和 / 二次剩余 / 递推公式

Key words

character sums / generalized Gauss sums / quadratic residues / recurrence formulas

参考文献

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基金资助

陕西数理基础科学研究项目(23JSQ041)