Frobenius distributions of Drinfeld modules over finite fields

Gekeler, Ernst-Ulrich

doi:10.1090/S0002-9947-07-04558-8

Frobenius distributions of Drinfeld modules over finite fields
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Trans. Amer. Math. Soc. 360 (2008), 1695-1721 Request permission

Abstract:

We express the weighted class number of Drinfeld $A$-modules of rank two with given characteristic polynomial over the finite field ${\mathbb {F}} _{\mathfrak {p}}=A/{\mathfrak {p}}$ $({\mathfrak {p}} \in \operatorname {Spec}A$, where $A=\mathbb {F} _q[T])$ as an infinite product of local terms. Some auxiliary results of independent interest about characteristic polynomials of Drinfeld modules are given.

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