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 ζ(s) α for 0 < q ≤ 1/2 and 0 < α < 1, completing the results of Bondarenko, Heap and Seip, and of Gerspach. Our results also apply to more general Euler products satisfying certain conditions.