A note on r$r$‐gaps between zeros of the Riemann zeta‐function

Abstract

AbstractIn this paper, we prove Selberg's announced result on ‐gaps between zeros of the Riemann zeta‐function . Our proof uses a result on variations of by Tsang based on Selberg's method. The same result with explicit constants under the Riemann Hypothesis has been obtained by Conrey and Turnage‐Butterbaugh using a different method. We explain how to obtain explicit constants under the Riemann Hypothesis using our approach which is based on Selberg's and Tsang's arguments.