Hecke Operators on Drinfeld Cusp Forms

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In this paper, we study the Drinfeld cusp forms for $Γ_1(T)$ and $Γ(T)$ using Teitelbaum's interpretation as harmonic cocycles. We obtain explicit eigenvalues of Hecke operators associated to degree one prime ideals acting on the cusp forms for $Γ_1(T)$ of small weights and conclude that these Hecke operators are simultaneously diagonalizable. We also show that the Hecke operators are not diagonalizable in general for $Γ_1(T)$ of large weights, and not for $Γ(T)$ even of small weights. The Hecke eigenvalues on cusp forms for $Γ(T)$ with small weights are determined and the eigenspaces characterized.
28 pages To appear in JNT

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Number Theory, 11F52; 20E08

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http://salesiana.dossiersoluciones.com/handle/123456789/158899

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0702742
 http://arxiv.org/abs/math/0702742

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arXiv