The Lindelöf Hypothesis for zeta zero ordinates

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发表日期：

2025年9月16日

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Ramūnas Garunkštis,
Athanasios Sourmelidis,
Jörn Steuding

摘要

We provide conditional and unconditional asymptotic formulae for the exponential sums $\sum _\gamma \,\gamma ^{-i\tau }$ $\sum_{γ} γ^{- i τ}$ , where the summation is over the ordinates of the nontrivial zeros $\rho =\beta +i\gamma $ $ρ = β + i γ$ of the Riemann zeta-function. In particular, the obtained results are related to the Lindelöf Hypothesis for these ordinates (in the sense of Gonek et al. in Proc AMS 148:2863–2875, 2020).