We study the action of Atkin U_t-operator on Drinfeld cusp forms for Γ_1(t) and Γ(t) using Teitelbaum’s interpretation as harmonic cocycles. For small weights k≤2q, we provide eigenvalues and eigenforms and prove U_t is diagonalizable in odd characteristic, pointing out that non-diagonalizability in even characteristic depends on antidiagonal blocks.

On the Atkin U_t-operator for Γ_1(t)-invariant Drinfeld cusp forms

Andrea Bandini;
2018

Abstract

We study the action of Atkin U_t-operator on Drinfeld cusp forms for Γ_1(t) and Γ(t) using Teitelbaum’s interpretation as harmonic cocycles. For small weights k≤2q, we provide eigenvalues and eigenforms and prove U_t is diagonalizable in odd characteristic, pointing out that non-diagonalizability in even characteristic depends on antidiagonal blocks.
Bandini, Andrea; Valentino, Maria
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/932898
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