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

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.
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Aleksandar Ivić. On mean value results for the Riemann zeta-function in short intervals.. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2009, Volume 32 - 2009, pp.4-23. ⟨10.46298/hrj.2009.164⟩. ⟨hal-01112342⟩

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