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

hrj:164 - Hardy-Ramanujan Journal, January 1, 2009, Volume 32 - 2009 - https://doi.org/10.46298/hrj.2009.164
On mean value results for the Riemann zeta-function in short intervals.

Authors: Aleksandar Ivić

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.

Volume: Volume 32 - 2009
Published on: January 1, 2009
Imported on: March 3, 2015
Keywords: mean values, Riemann zeta-function, short intervals, critical strip, critical line,[MATH] Mathematics [math]