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arXiv · 2505.24748

Equidistribution and arithmetic $\Lambda$-distributions

Matthew Bertucci·Sean Howe
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Abstract

We formulate an abstract notion of equidistribution for families of $\lambda$-probability spaces parameterized by admissible $\mathbb{Z}$-sets. Under the assumption of equidistribution, we show that the $\sigma$-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 $\Lambda$-distributions for several natural families of function field $L$-functions and zeta functions.

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Matthew Bertucci, Sean Howe. 2025-05-30. Equidistribution and arithmetic $\Lambda$-distributions. https://arxiv.org/abs/2505.24748

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