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On moments of $|ζ(1/2+it)|$ in short intervals

Aleksandar Ivić
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Abstract

Power moments of $$ J_k(t,G) = {1\over\sqrtπG} \int_{-\infty}^\infty |ζ(1/2 + it + iu)|^{2k}{\rm e}^{-(u/G)^2} du \qquad(t \asymp T, T^ε\le G \ll T),$$ where $k$ is a natural number, are investigated. The results that are obtained are used to show how bounds for $\int_0^T|ζ(1/2+it)|^{2k} dt$ may be obtained.

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Aleksandar Ivić. 2004-04-16. On moments of $|ζ(1/2+it)|$ in short intervals. https://arxiv.org/abs/math/0404289

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