Riemann—ζ函数的一个新均值定理的应用

SOME APPLICATION OF A NEW MEAN VALUE THEOREM ON RIEMANN—ζ FUNCTION

Deshonillers和Iwaniec[1]给出了Riemann—ζ函数的一个新均值定理,本文将这个定理用于讨论Dirichlet级数之和的估计,并得到了此[2]、[3]更好的结果。如果将这些估计式用于相邻素数差问题,则可以改进[3]的结果。

Deshouillers and Iwaniee have proved a new mean value theorem on Riemann-ζ function. In this paper, We discuss the estimation of the sum on Dirichlet's Series We obtain the estimation of (1) that is better than the estimation in[2] and[3].