On sums of squares of $|\zeta(\frac12+i\gamma)|$ over short intervals

zbMATH Open1413.11098arXiv1801.01289MaRDI QIDQ4684621

Aleksandar Ivić

Publication date: 24 September 2018

Abstract: A discussion involving the evaluation of the sum ${\displaystyle }$sum_{T<gle T+H}|zeta(1/2+igamma)|^2${\displaystyle }$ and some related integrals is presented, where $gamma,(>0)$ denotes imaginary parts of complex zeros of the Riemann zeta-function $zeta(s)$. It is shown unconditionally that the above sum is $,llHlo{g}^{2}TloglogT,$ for $,T^{2/3}lo{g}^{4}TllHleT$.

Full work available at URL: https://arxiv.org/abs/1801.01289

zbMATH Keywords

Riemann zeta-functionshort intervalsdiscrete mean square estimates

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Zeta and (L)-functions: analytic theory (11M99)

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