PreprintCC BY 4.0arXiv
Lower bounds for discrete moments in a conjecture of Ng
Abstract
Assuming the Riemann Hypothesis and the simplicity of the non-trivial zeros of the Riemann zeta function ζ(s), we prove lower bounds for the discrete moments ∑0<γ≤ T|ζ(2ρ)/ζ'(ρ)|2k for every fixed rational k≥1, and for every fixed real k≥1. At k=1 we give a new proof of the explicit bound, half of the main term conjectured by Ng.
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BibTeX
@misc{pearcecrump2026lower,
title = {{Lower bounds for discrete moments in a conjecture of Ng}},
author = {Andrew Pearce-Crump},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.12376},
eprint = {2606.12376},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.12376},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Lower bounds for discrete moments in a conjecture of Ng
AU - Andrew Pearce-Crump
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2606.12376
UR - https://arxiv.org/abs/2606.12376
AB - Assuming the Riemann Hypothesis and the simplicity of the non-trivial zeros of the Riemann zeta function ζ(s), we prove lower bounds for the discrete moments ∑_0<γ≤ T|ζ(2ρ)/ζ'(ρ)|^2k for every fixed rational k≥1, and for every fixed real k≥1. At k=1 we give a new proof of the explicit bound, half of the main term conjectured by Ng.
ER -