Asymmetry of Generalized $ζ$ Functions under the Rotation Number Hypothesis
Authors: Walid Oukil
Abstract: In this manuscript, we show that the Riemann zeta function satisfies $\big(ζ(s),ζ(1-\overline{s})\big)\neq(0,0)$ for any $s$ in the critical strip, except on the critical line. This still holds even when the fractional part function is replaced by a function satisfying a specific \textit{Rotation Number Hypothesis}.
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