Equidistribution and arithmetic Λ-distributions

2025/05/30 by Bertucci, Matthew, Howe, Sean
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.24748

Abstract

We formulate an abstract notion of equidistribution for families of λ-probability spaces parameterized by admissible 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.

Citations

• Zeta statistics and Hadamard functions
• Motivic Euler products in motivic statistics
• Motivic Euler products and motivic height zeta functions
• The probability that a complete intersection is smooth

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