Low pseudomoments of Euler products

Abstract

In this paper, we determine the order of magnitude of the $2q$-th pseudomoment of powers of the Riemann zeta function $\zeta (s{)}^{\alpha }$ for $0<q\le 1/2$ and $0<\alpha <1$, completing the results of Bondarenko, Heap and Seip, and of Gerspach. Our results also apply to more general Euler products satisfying certain conditions.

21 pages