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广义高阶Bernoulli数,Gauss和及广义Kloosterman和(英文)
引用本文:张小蹦,刘华宁.广义高阶Bernoulli数,Gauss和及广义Kloosterman和(英文)[J].数学进展,2011(3).
作者姓名:张小蹦  刘华宁
作者单位:西安邮电学院应用数理系;西北大学数学系;
基金项目:supported by the Natural Science Foundation of the Education Department of Shaanxi Province of China(No.08JK437)
摘    要:利用广义高阶Bernoulli数的性质及Dirichlet L-函数的均值定理,研究了Gauss和及广义Kloosterman和与广义高阶Bernoulli数的均值性质,并给出两个有趣的渐近公式.

关 键 词:Gauss和  广义Kloosterman和  广义高阶Bernoulli数  渐近公式  

Mean Value of Higher Order Generalized Bernoulli Numbers,Gauss Sums and General Kloosterman Sums
ZHANG Xiaobeng,LIU Huaning.Mean Value of Higher Order Generalized Bernoulli Numbers,Gauss Sums and General Kloosterman Sums[J].Advances in Mathematics,2011(3).
Authors:ZHANG Xiaobeng  LIU Huaning
Institution:ZHANG Xiaobeng~(1,*),LIU Huaning~2 (1.Department of Applied Mathematics and Physics,Xi'an University of Post and Telecommunications,Xi'an,Shaanxi,710121,P.R.China,2.Department of Mathematics,Northwest University,710127,P.R.China)
Abstract:The main purpose of this paper is using the properties of higher order generalized Bernoulli numbers and the mean value theorems of Dirichlet L-function to study the mean value of Gauss sums,general Kloosterman sums and higher order generalized Bernoulli numbers,and give two interesting asymptotic formulae for it.
Keywords:Gauss sum  general Kloosterman sum  higher order generalized Bernoulli number  asymptotic formulae  
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