On zeroes and poles of Helson zeta functions

I. Bochkov; R. Romanov

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arXiv · 2106.15949

On zeroes and poles of Helson zeta functions

I. Bochkov·R. Romanov

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Abstract

We show that the analytic continuations of Helson zeta functions $ \zeta_\chi (s)= \sum_1^{\infty}\chi(n)n^{-s} $ can have essentially arbitrary poles and zeroes in the strip $ 21/40 < \Re s < 1 $ (unconditionally), and in the whole critical strip $ 1/2 < \Re s <1 $ under Riemann Hypothesis.

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I. Bochkov, R. Romanov. 2021-06-30. On zeroes and poles of Helson zeta functions. https://arxiv.org/abs/2106.15949

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