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arXiv · 2505.14228

The Lindel\"of Hypothesis for Zeta Zero Ordinates

Ramūnas Garunkštis·Athanasios Sourmelidis·Jörn Steuding
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Abstract

We provide conditional and unconditional asymptotic formulae for the exponential sums $\sum_\gamma\,\gamma^{-i\tau}$, where the summation is over the ordinates of the nontrivial zeros $\rho=\beta+i\gamma$ of the Riemann zeta-function. In particular, the obtained results are related to the Lindel\"of Hypothesis for these ordinates (in the sense of Gonek et al. [10]).

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Ramūnas Garunkštis, Athanasios Sourmelidis, Jörn Steuding. 2025-05-20. The Lindel\"of Hypothesis for Zeta Zero Ordinates. https://doi.org/10.1007/s11139-025-01208-1

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