Matrix group $Λ$-distributions

Abstract

The $Λ$-distribution of a compact matrix group is an invariant in algebraic probability theory that was recently introduced to study zero distributions of function field $L$-functions. It is encoded by the $σ$-moment generating function, a generalization of the Molien series of classical invariant theory. In this work, we compute the $σ$-moment generating functions of finite matrix groups in many new cases. In particular, we compute the asymptotic $Λ$-distributions for the infinite families of Weyl reflection groups of types $B_n/C_n$