On the Riemann zeta-function and the divisor problem II

Details On the Riemann zeta-function and the divisor problem II On the Riemann zeta-function and the divisor problem II

2004-11-18

arxiv.org/abs/math/0411404v2

Central European Journal of Mathematics 3(2) (2005), 203-214

Mathematics

Number Theory

13 pages

Scientific paper

First part of this paper was published in CEJM (2)(4) (2004), 1-15. It is proved now that $$ \int_0^T|E^*(t)|^5{\rm d}t \ll_\epsilon T^{2+\epsilon}. $$ Here $$ E^*(t) = E(t) - 2\pi\Delta^*(t/2\pi), \Delta^*(x) = - \Delta(x) +2\Delta(2x) - {1\over2}\Delta(4x), $$ where $E(t)$ is the error term in the mean square formula for $|\zeta(1/2+it)|$ and $\Delta(x)$ is the error term in the Dirichlet divisor problem. It is also shown how bounds for moments of $|E^*(t)|$ lead to bounds for moments of $|\zeta(1/2+it)|$.

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