Mathematics – Number Theory
Scientific paper
2006-11-14
Acta Math. Hung. 119(2008), 15-24
Mathematics
Number Theory
9 pages
Scientific paper
Some new results on power moments of the integral $$ J_k(t,G) =
{1\over\sqrt{\pi}G} \int_{-\infty}^\infty |\zeta(1/2 + it + iu)|^{2k}{\rm
e}^{-(u/G)^2}du \qquad(t \asymp T, T^\epsilon \le G \ll T, k\in\N) $$ are
obtained when $k=1$. These results can be used to derive bounds for moments of
$|\zeta(1/2+it)|$.
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