广义三项指数和六次均值的显式公式  

Explicit formula for sixth power mean of the generalized three-term exponential sums

作　　者：张雨濛 张天平 ZHANG Yumeng;ZHANG Tianping(School of Mathematics and Statistics,Shaanxi Normal University,Xi'an 710119,China)

机构地区：[1]陕西师范大学数学与统计学院,陕西西安710119

出　　处：《纯粹数学与应用数学》2025年第1期89-97,共9页Pure and Applied Mathematics

基　　金：国家自然科学基金(12271320,11871317);陕西省杰出青年科学基金(2021JC-29).

摘　　要：三项指数和是数论的研究重要对象.由于这类和式的单个上界估计十分困难,本文转而从均值的角度研究了广义三项指数和的六次均值问题.利用初等方法以及同余方程组解的性质,本文给出了一些有趣的显式公式,所得结果丰富和完善了三项指数和的相关研究.Three-term exponential sums are one of significant objects of study in number theory.Due to the inherent complexity in establishing a uni ed upper bound for such sums,we turn to investigate the sixth power mean of the generalized three-term exponential sums through the application of mean value method.By using the elementary methods and the properties of solutions to congruence equations,some explicit formulas are given,which enrich the related research on three-term exponential sums.

关 键 词：三项指数和 六次均值 初等方法 显式公式 

分 类 号：O156.4[理学—数学]