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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