Mean values of the Riemann zeta function at shifted zeros under the Riemann Hypothesis

Ramūnas Garunkštis, Julija Paliulionytė

Assuming the Riemann hypothesis, we obtain asymptotic formulas for ${\sum }_{0<\gamma <T}\zeta (\rho +\delta )\zeta (1-\rho +\overline{\delta })$ in the region $-\frac{a}{\log T} \leq \Re δ\leq \frac{1}{2}+\frac{a}{\log T…