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arXiv · 1702.08801

On the diagonalizability of the Atkin U-operator for Drinfeld cusp forms

Andrea Bandini·Maria Valentino
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Abstract

We study the diagonalizability of the Atkin $U$-operator acting on Drinfeld cusp forms for $\Gamma_1(t)$ and $\Gamma(t)$ using Teitelbaum's interpretation as harmonic cocycles. We prove $U$ is diagonalizable for small weights and explicitly compute the eigenvalues. We also formulate a conjecture, supported by numerical search and proofs in some special cases, about non diagonalizability of $U$ in even characteristic.

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Andrea Bandini, Maria Valentino. 2017-02-28. On the diagonalizability of the Atkin U-operator for Drinfeld cusp forms. https://arxiv.org/abs/1702.08801

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