首页 | 本学科首页   官方微博 | 高级检索  
     


Mean value of mixed exponential sums
Authors:Huaning Liu
Affiliation:Department of Mathematics, Northwest University, Xi'an, Shaanxi, People's Republic of China
Abstract:For integers $ q$, $ m$, $ n$, $ k$ with $ q,kgeq 1$, and Dirichlet character $ chibmod q$, we define a mixed exponential sum

$displaystyle C(m,n,k,chi;q):= mathop{{sum}'}_{a=1}^qchi(a)hbox{e}left(frac{ma^k+na}{q}right), $

where $ displaystyle hbox{e}(y)=hbox{e}^{2pi iy}$, and $ sum'_{a}$ denotes the summation over all $ a$ with $ (a,q)=1$. The main purpose of this paper is to study the mean value of

$displaystyle sum_{chibmod q}mathop{{sum}'}_{m=1}^qleftvert C(m,n,k,chi;q)rightvert^4, $

and to give a related identity on the mean value of the general Kloosterman sum

$displaystyle K(m,n,chi;q):=mathop{{sum}'}_{a=1}^qchi(a)hbox{e}left(frac{ma +noverline{a}}{q}right), $

where $ aoverline{a} equiv 1 bmod q$.

Keywords:Exponential sum   Kloosterman sum   mean value   identity.
点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
点击此处可从《Proceedings of the American Mathematical Society》下载全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号