Some Remarks on the Mean-Value of the Riemann Zeta-Function and other Dirichlet Series-IV

The object of this paper is to prove the following theorem.

Theorem 1. Let α and k be real numbers subject to 1/2+q(log H)^-1≤α≤2 (where q is a positive integer to be defined presently) and δ≤k≤δ^-1 where δ is any positive constant.