On zeroes and poles of Helson zeta functions

摘要

We show that the analytic continuations of Helson zeta functions zeta(chi)(s) = Sigma(infinity)(1) chi(n)n(-s) can have essentially arbitrary poles and zeroes in the strip 21/40 < Rs < 1 (unconditionally), and in the whole critical strip 1/2 < Rs < 1 under Riemann Hypothesis. (c) 2022 Elsevier Inc. All rights reserved.