Year: 2026
Type: preprint
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 $\sum_{0<γ\le T}|ζ(2ρ)/ζ'(ρ)|^{2k}$ for every fixed rational $k\ge1$, and for every fixed real $k\ge1$. At $k=1$ we give a new proof of the explicit bound, half of the main term conjectured by Ng.
Source: arXiv (Cornell University)
Author: Pearce-Crump, Andrew
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7164397166