We show that the analytic continuations of Helson zeta functions ζχ(s)=∑1χ(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.

Translated title of the contributionО нулях и полюсах дзета-функции Хелсона
Original languageEnglish
Article number109398
JournalJournal of Functional Analysis
Volume282
Issue number8
DOIs
StatePublished - 15 Apr 2022

    Scopus subject areas

  • Analysis

    Research areas

  • Dirichlet series, Helson zeta function, Meromorphic extension

ID: 98050016