关于两类特征和的递推性质

doi:10.6040/j.issn.1671-9352.0.2025.333

《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (4): 69-77.doi: 10.6040/j.issn.1671-9352.0.2025.333

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关于两类特征和的递推性质

王啸

长安大学理学院, 陕西西安 710064

发布日期:2026-04-08
基金资助:
陕西数理基础科学研究项目(23JSQ041)

Two kinds of character sums and their recurrence properties

WANG Xiao

School of Science, Changan University, Xian 710064, Shaanxi, China

Published:2026-04-08

摘要/Abstract

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。

关键词: 特征和, 广义Gauss和, 二次剩余, 递推公式

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.

Key words: character sums, generalized Gauss sums, quadratic residues, recurrence formulas

中图分类号:

O156.4

王啸. 关于两类特征和的递推性质[J]. 《山东大学学报(理学版)》, 2026, 61(4): 69-77.

WANG Xiao. Two kinds of character sums and their recurrence properties[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(4): 69-77.

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关于两类特征和的递推性质

Two kinds of character sums and their recurrence properties

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