On a conjecture of Chowla and Walum

作     者：TANIGAWA Yoshio 

作者机构：Graduate School of of MathematicsNagoya University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2010年第53卷第10期

页      面：2755-2771页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by National Natural Science Foundation of China (Grant No.10771127) Research Award Foundation for Young Scientists of Shandong Province (Grant No.BS2009SF018) 

主　　题：the Dirichlet divisor problem error term mean square the Bernoulli polynomial the Vorono formula Chowla and Walum’s conjecture. 

摘      要：We show the asymptotic behaviour of the mean square of the sum n c√x naPk(x/n),where Pk(x) = Bk({x}) and Bk(x) denotes the Bernoulli polynomial of degree k and c 0 is a real number such that c2 is *** result implies that a conjecture of Chowla and Walum is true on average.