Upper bounds on a two-term exponential sum  

作　　者：Todd COCHRANE 郑志勇 

机构地区：[1]Department of Mathematics, Kansas State University, Manhattan, KS 66506, USA [2]Department of Mathematics, Tsinghua University, Beijing 100084, China

出　　处：《Science China Mathematics》2001年第8期1003-1015,共13页中国科学：数学（英文版）

基　　金：Tsinghua University and the NNSF of China for supporting his visit to China during the Fall of 2000;This work was supported by the National Natural Science Foundation of China (Grant No. 19625102).

摘　　要：We obtain upper bounds for mixed exponential sums of the type $S(\chi ,f,p^m ) = \sum\nolimits_{x = 1}^{p^n } {\chi (x)e} _{p^m } (ax^n + bx)$ where pm is a prime power with m? 2 and X is a multiplicative character (mod pm). If X is primitive or p?(a, b) then we obtain |S(χ,f,p m)| ?2np 2/3 m . If X is of conductor p and p?( a, b) then we get the stronger bound |S(χ,f,p m)|?np m/2.We obtain upper bounds for mixed exponential sums of the type S(x,f,pm) =bx)where pm is a prime power with m ≥ 2 and x is a multiplicative character 2(mod pm). If x is primitive or p\( a, b) then we obtain ｜ S(x, f, pm) ｜ ≤2np2-3m. If x is of conductor p and p\( a, b) then we get the stronger bound ｜ S(x, f, pm) ｜ ≤ npm/2.

关 键 词：exponential sums primitive character weil’sbound 

分 类 号：O156[理学—数学]