Equidistribution and arithmetic $\hat{I}›$-distributions

Abstract

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

32 pages, comments welcome