Frobenius distributions of Drinfeld modules over finite fields
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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.References
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Additional Information
- Ernst-Ulrich Gekeler
- Affiliation: FR 6.1 Mathematik, Universität des Saarlandes, Postfach 15 11 50, D-66041 Saar- brücken, Germany
- Email: gekeler@math.uni-sb.de
- Received by editor(s): March 16, 2005
- Published electronically: November 26, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 1695-1721
- MSC (2000): Primary 11G09
- DOI: https://doi.org/10.1090/S0002-9947-07-04558-8
- MathSciNet review: 2366959