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 广义伯努利数、广义Kloosterman和与特征和 Mean Value of Generalized Bernoulli Numbers, General Kloosterman Sums and Character Sums 张小蹦1, 刘华宁2 ZHANG Xiaobeng1,*, LIU Huaning2,** 1.西安邮电大学理学院，西安，陕西，710121; 2. 西北大学数学系，西安，陕西，701127 1. School of Science, Xi'an University of Post and Telecommunications, Xi'an, Shaanxi, 710121, P. R. China; 2. Department of Mathematics, Northwest University, Xi'an, Shaanxi, 710127, P. R. China 收稿日期: 2011-06-20 出版日期: 2013-10-25 DOI: 10.11845/sxjz.20130510
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 摘要 作为不完整特征和的应用, 本文利用特征和估计, Ramanujan和及Dirichlet $L$-函数均值定理研究了广义伯努利数、广义Kloosterman和与不完整特征和的值分布性质, 并给出了两个渐近公式. 关键词 ： 特征和,  广义伯努利数,  广义Kloosterman和 Abstract：As an application of incomplete character sums, we use estimates for character sums, Ramanujan's sum and the mean value theorem of the Dirichlet $L$-function to study the distribution properties of generalized Bernoulli numbers and general Kloosterman sums weighted by incomplete character sums, and give two interesting asymptotic formulae for it. Key words： generalized Bernoulli numbers    general Kloosterman sums 基金资助:This work is supported by NSFC (No. 10901128) and the Natural Science Foundation of the Education Department of Shaanxi Province of China (No. 13JK0560).
 [1] 林馨. 6次高斯和与广义Kloosterman和的混合均值[J]. 数学进展, 2019, 48(3): 315-324. [2] 张小蹦, 刘华宁. 广义高阶 Bernoulli 数, Gauss和及广义Kloosterman 和 (英)[J]. 数学进展, 2011, 40(3): 373-383.
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