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

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

2004-04-16

arxiv.org/abs/math/0404289v1

Ramanujan Math. Soc. LNS 2, The Riemann zeta function and related themes, eds. R. Balasubramanian and K. Srinivas, 2006, 81-97

Mathematics

Number Theory

20 pages

Scientific paper

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

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