The Lindelöf Hypothesis for Zeta Zero Ordinates

2025/05/20 by Garunkštis, Ramūnas, Sourmelidis, Athanasios, Steuding, Jörn
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.14228

Abstract

We provide conditional and unconditional asymptotic formulae for the exponential sums ∑_γ γ^-iτ, where the summation is over the ordinates of the nontrivial zeros ρ=β+iγ 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. [10]).

Citations

• On certain sums over ordinates of zeta zeros
• Remarks on the generalized Lindelöf Hypothesis

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