On the moments of the Riemann zeta-function near the critical line
The author considers \[ I_k (\sigma,T) = \int^T_1 \bigl|\zeta(\sigma+it) \bigr |^{2k} dt \] for \({1\over 2} < \sigma < 1\), \(k\geq 0\) and \(T\geq 2\). He shows that \[ I_k (\sigma, T) \gg_kT \left\{\min \left(\log T, {1\over \sigma - {1\over 2}} \right) \right\}^{k^2} \] for all rational \(k\), uniformly in \(\sigma\). On the Riemann hypothesis he shows that both the above bound and the corresponding upper bound hold for all real \(k\geq 0\). In the latter case explicit constants are given. The methods follow those of the reviewer [J. Lond. Math. Soc., II. Ser. 24, 65-78 (1981; Zbl 0454.10025)] and [Q. J. Math., Oxf. II. Ser. 44, 185-197 (1993; Zbl 0798.11031)] in detail.
fractional moments of the Riemann zeta-function near the critical line
scientific article; zbMATH DE number 939532
scientific article