The Hybrid Power Mean Involving the Character Sum of Polynomials and a Sum Analogous to Kloosterman Sum  

多项式特征和与类Kloosterman和的混合均值问题

作　　者：LU Xingxing ZHANG Wenpeng 吕星星;张文鹏(西安建筑科技大学理学院,陕西西安710055;西北大学数学学院数论及其应用研究中心,陕西西安710127)

机构地区：[1]School of Science,Xi'an University of Architecture and Technology,Xi'an,Shaanxi,710055,P.R.China [2]Research Center for Number Theory and Its Applications,School of Mathematics,Northwest University,Xi'an,Shaanxi,710127,P.R.China

出　　处：《数学进展》2024年第6期1199-1209,共11页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.12126357);Natural Science Basic Research Plan in Shaanxi Province of China(No.2023-JC-QN-0058)。

摘　　要：The main purpose of this paper is using the properties of the classical Gauss sum and the analytic methods to study the computational problem of one kind of hybrid power mean involving the character sum of polynomials and a sum analogous to Kloosterman sum mod p,an odd prime,and give two sharp asymptotic formulae for them.本文主要目的是利用经典Gauss和的性质及解析的方法研究模p意义下的多项式特征和与类Kloosterman和的混合均值计算问题,最后给出该均值的两个精确的渐近公式.

关 键 词：character sum of polynomials a sum analogous to Kloosterman sum hybrid power mean the classical Gauss sum analytic method asymptotic formula 

分 类 号：O156.4[理学—数学]