On mean value results for the Riemann zeta-function in short intervals.

Aleksandar Ivić

Type: Article

Publication Date: 2009-01-01

Citations: 11

DOI: https://doi.org/10.46298/hrj.2009.164

Abstract

We discuss the mean values of the Riemann zeta-function $\zeta(s)$, and analyze upper and lower bounds for $$\int_T^{T+H} \vert\zeta(\frac{1}{2}+it)\vert^{2k}\,dt~~~~~~(k\in\mathbb{N}~{\rm fixed,}~1<\!\!< H \leq T).$$ In particular, the author's new upper bound for the above integral under the Riemann hypothesis is presented.

Locations

HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF
Hardy-Ramanujan Journal - View - PDF

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