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.File in questo prodotto:
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