On the Higher Moments of Coefficients Attached to Dedekind Zeta Function  

戴德金zeta函数系数的高阶均值估计

作　　者：HUA Guodong 华国栋(渭南师范学院数学与统计学院,陕西渭南714099;山东大学数学学院,山东济南250100)

机构地区：[1]School of Mathematics and Statistics,Weinan Normal University,Weinan,Shaanci,714099,P.R.China [2]School of Mathematics,Shandong University,Jinan,Shandong,250100,P.R.China

出　　处：《数学进展》2024年第6期1188-1198,共11页Advances in Mathematics（China）

基　　金：Supported in part by NSFC (Nos.12401011,12201214);National Key Research and Development Program of China (No.2021YFA1000700);Natural Science Basic Research Program of Shaanxi (Nos.2023-JC-QN-0024,2023-JC-YB-077);Foundation of Shaanxi Educational Committee (No.2023-JCYB-013);Shaanxi Fundamental Science Research Project for Mathematics and Physics (Nos.23JSQ053,22JSQ010);Scientific Research Foundation of WNU。

摘　　要：Let K_(3) be a non-normal cubic extension over Q.In this paper,we investigate the higher moments of the coefficients a_(K_(3))(n) of Dedekind zeta function over sum of two squares of the following types■ where l≥9 is any fixed positive integer,which generalizes the results in [Front.Math.China,2020,15(1):57-67].令K_(3)是一个Q的非正规的三次扩张.本文考虑戴德金zeta函数系数a_(K_(3))(n)在表两平方数求和序列上如下类型的高阶均值■其中l≥9是一个任意固定的正整数,推广了[Front.Math.China,2020,15(1):57-67]的结论.

关 键 词：non-normal cubic field Dedekind zeta function Rankin-Selberg L-function 

分 类 号：O156.4[理学—数学]