Mean-value theorem of Riemann zeta-function over short intervals
Assuming the Riemann hypothesis, the authors obtain an asymptotic formula for the mean-square of \(\zeta(\sigma+it)\) over \((T,T+H)\), provided \(1/2+ c/\log\log T\leq\sigma\leq 1-\delta\) and \(Y\leq H\leq T\), where \(Y=\exp((\log T)^{2-2\sigma})\) and \(c,\delta>0\). The proof is based on a mean-value theorem for Dirichlet polynomials.
scientific article; zbMATH DE number 483992