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arXiv · 2411.08863

Probability Laws Concerning Zeta Integrals

Grayson Plumpton
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Abstract

We give a probabilistic interpretation of the Dedekind zeta functions of $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-2})$ using zeta integrals and use this to show that the first two Li coefficients of these zeta functions are positive. This extends a result of Biane, Pitman, and Yor (2001) which considered the case of the Riemann zeta function.

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Grayson Plumpton. 2024-11-13. Probability Laws Concerning Zeta Integrals. https://arxiv.org/abs/2411.08863

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