关于Hurwitz zeta-函数的四次均值(英文)

ON THE FOURTH POWER MEAN OF HURWITZ ZETA-FUNCTION

对s=σ+it,ζ(s,α)是Hurwitz zeta-函数,ζ_1(s,α)=ζ(sα)-α^(-3)。本文的主要目的是用解析的方法给出了Hurwitz zeta-函数四次均值较强的渐近公式 integral from n=0 to 1[(|ζ_1(1+it,α)|~4dα]

For s =σ +it, letξ (s,α ) be Hurwitz zeta-function, ξ1(s,α ) =ξ(s,α) -α-s. The main purpose of this paper is using the analytic method to give a sharper asymptotic formula for the fourth power mean of Hurwitz zeta-function