Mean-Value Theorem of the Riemann Zeta-Function Over Short Intervals Original Research Article

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.