Equidistribution and arithmetic $Λ$-distributions
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908386418753536 |
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| author | Bertucci, Matthew Howe, Sean |
| author_facet | Bertucci, Matthew Howe, Sean |
| contents | We formulate an abstract notion of equidistribution for families of $λ$-probability spaces parameterized by admissible $\mathbb{Z}$-sets. Under the assumption of equidistribution, we show that the $σ$-moment generating functions of certain infinite sums of random variables can be computed as motivic Euler products. Combining this result with earlier generalizations of Poonen's sieve, we compute the asymptotic $Λ$-distributions for several natural families of function field $L$-functions and zeta functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24748 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equidistribution and arithmetic $Λ$-distributions Bertucci, Matthew Howe, Sean Number Theory Algebraic Geometry We formulate an abstract notion of equidistribution for families of $λ$-probability spaces parameterized by admissible $\mathbb{Z}$-sets. Under the assumption of equidistribution, we show that the $σ$-moment generating functions of certain infinite sums of random variables can be computed as motivic Euler products. Combining this result with earlier generalizations of Poonen's sieve, we compute the asymptotic $Λ$-distributions for several natural families of function field $L$-functions and zeta functions. |
| title | Equidistribution and arithmetic $Λ$-distributions |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2505.24748 |