Zeta Regularized Trigonometric Products Over Zeros Of The Riemann Zeta Function

Efe Gürel

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arXiv · 2505.00723

Zeta Regularized Trigonometric Products Over Zeros Of The Riemann Zeta Function

Efe Gürel

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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.

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Efe Gürel. 2025-11-11. Zeta Regularized Trigonometric Products Over Zeros Of The Riemann Zeta Function. https://arxiv.org/abs/2505.00723

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