Probability Laws Concerning Zeta Integrals
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916479535939584 |
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| author | Plumpton, Grayson |
| author_facet | Plumpton, Grayson |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08863 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Probability Laws Concerning Zeta Integrals Plumpton, Grayson Number Theory Probability 11R42 (primary), 11R56 (primary), 60B15 (secondary) 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. |
| title | Probability Laws Concerning Zeta Integrals |
| topic | Number Theory Probability 11R42 (primary), 11R56 (primary), 60B15 (secondary) |
| url | https://arxiv.org/abs/2411.08863 |