The Uniform Distribution Modulo One of Certain Subsequences of Ordinates of Zeros of the Zeta Function

Autor: Çiçek, Fatma, Gonek, Steven M.
Rok vydání: 2023
Předmět:
Zdroj: Math. Proc. Camb. Phil. Soc. 176 (2024) 593-608
Druh dokumentu: Working Paper
DOI: 10.1017/S0305004124000045
Popis: On the assumption of the Riemann hypothesis and a spacing hypothesis for the nontrivial zeros $\frac12+i\gamma$ of the Riemann zeta function, we show that the sequence \[ \Gamma_{[a, b]} =\Bigg\{ \gamma : \gamma>0 \quad \mbox{and} \quad \frac{ \log\big(| \zeta^{(m_{\gamma})} (\frac12+ i\gamma) | / (\log{\gamma})^{m_{\gamma}}\big)}{\sqrt{\frac12\log\log{\gamma}}} \in [a, b] \Bigg\}, \] where the $\gamma$ are arranged in increasing order, is uniformly distributed modulo one. Here $a$ and $b$ are real numbers with $a
Databáze: arXiv
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