Hecke operators on Drinfeld cusp forms

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Abstract

In this paper, we study the Drinfeld cusp forms for Γ1 (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 Γ1 (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 Γ1 (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. © 2008 Elsevier Inc. All rights reserved.

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Li, W. C. W., & Meemark, Y. (2008). Hecke operators on Drinfeld cusp forms. Journal of Number Theory, 128(7), 1941–1965. https://doi.org/10.1016/j.jnt.2008.02.008

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