We study the action of Atkin Ut-operator on Drinfeld cusp forms for τ1 (t) and τ(t) using Teitelbaum's interpretation as harmonic cocycles. For small weights k ≤ 2q, we provide eigenvalues and eigenforms and prove Ut is diagonalizable in odd characteristic, pointing out that non-diagonalizability in even characteristic depends on antidiagonal blocks.

On the Atkin Ut-operator for τ1 (t)-invariant Drinfeld cusp forms

Bandini A.;Valentino M.
2018-01-01

Abstract

We study the action of Atkin Ut-operator on Drinfeld cusp forms for τ1 (t) and τ(t) using Teitelbaum's interpretation as harmonic cocycles. For small weights k ≤ 2q, we provide eigenvalues and eigenforms and prove Ut is diagonalizable in odd characteristic, pointing out that non-diagonalizability in even characteristic depends on antidiagonal blocks.
Atkin-Lehner operator
diagonalizability
Drinfeld cusp forms
harmonic cocycles
newforms and oldforms
slopes of eigenforms
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/341950
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