Mean-value theorem of the riemann zeta-function over short intervals

Abstract

Let s = σ + it. Then, on the assumption of Riemann Hypothesis, we prove the Mean-Value Theorem for the square of the Riemann zeta-function over shorter intervals for 1/2 + A1/log log T ≤ σ ≤ 1 - δ. Here A1 is a large positive constant, δ is a small positive constant, and T ≤ t ≤ T + H where H depends on T satisfying H ≤ T. © 1993 Academic Press Inc.