Asymptotical formula for fractional moments of some Dirichlet series

S. A. Gritsenko ; L. N. Kurtova

Čebyševskij sbornik, Tome 14 (2013) no. 1, pp. 18-33

Résumé

Let $v \in \mathbf{N}$. Let the function $\Phi(T)$ arbitrarily slow tend to $+\infty$ with $T \rightarrow +\infty $. The asymptotical formulas for fractional moments of the Riemann zeta-function $\int\limits_T^{2T}|\zeta(\sigma+it)|^{2/v}dt$ for ${1}/{2}+{\Phi(T)}/{\ln T}\le \sigma1$ and for fractional moments of the arithmetical Dirichlet series of second degree from Selberg's class $\int\limits_T^{2T}|L(\sigma+it)|^{2/v}dt$ for ${1}/{2}+{\Phi(T)}/{\sqrt{\ln T}}\le \sigma1$, are obtained.