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;
2018-01-01
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.File in questo prodotto:
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