Zeta Regularized Trigonometric Products Over Zeros Of The Riemann Zeta Function
Number Theory
2025-11-12 v2
Abstract
We prove a novel zeta regularized product formula concerning regularization of trigonometric products over non-trivial zeros of the Riemann zeta function. Furthermore, we calculate the discrepancies of such regularized products. In special cases, our formula reduces to the Kimoto-Wakayama formula. A conjectural relationship between such products and a weak Riemann hypothesis is speculated.
Keywords
Cite
@article{arxiv.2505.00723,
title = {Zeta Regularized Trigonometric Products Over Zeros Of The Riemann Zeta Function},
author = {Efe Gürel},
journal= {arXiv preprint arXiv:2505.00723},
year = {2025}
}
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12 pages