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 rational.Our res...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 rational.Our result implies that a conjecture of Chowla and Walum is true on average.展开更多
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)
文摘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 rational.Our result implies that a conjecture of Chowla and Walum is true on average.
