A note on r-gaps between zeros of the Riemann zeta-function
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY(2024)
Abstract
In this paper, we prove Selberg's announced result on r-gaps between zeros of the Riemann zeta-function zeta. Our proof uses a result on variations of arg zeta 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.
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Key words
zeros,zeta-function
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