Asymmetry  of Generalized $\zeta$ Functions under the Rotation Number Hypothesis

Walid OUKIL

doi:10.33774/coe-2025-97vw5-v10

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Asymmetry of Generalized $\zeta$ Functions under the Rotation Number Hypothesis

13 March 2026, Version 10

Working Paper

Walid OUKIL

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This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

In this manuscript, we prove that the Riemann zeta function satisfies $\big(\zeta(s),\zeta(1-\overline{s})\big)\neq(0,0)$ for any $s$ in the critical strip, even when the fractional part function is replaced by a function satisfying a specific \textit{Rotation Number Hypothesis}.

Keywords

Zeta function

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