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On mean values of some zeta-functions in the critical strip

Aleksandar Ivić
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Abstract

For a fixed integer $k\ge 3$ and fixed $1/2 < σ> 1$ we consider $$ \int_1^T |ζ(σ+ it)|^{2k}dt = \sum_{n=1}^\infty d_k^2(n)n^{-2σ}T + R(k,σ;T), $$ where $R(k,σ;T) = o(T) (T\to\infty)$ is the error term in the above asymptotic formula. Hitherto the sharpest bounds for $R(k,σ;T)$ are given for certain ranges of $σ$. We also obtain new mean value results for the zeta-functions of holomorphic cusp forms and the Rankin-Selberg series.

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Aleksandar Ivić. 2003-11-23. On mean values of some zeta-functions in the critical strip. https://arxiv.org/abs/math/0311403

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