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arXiv · 2502.17582

Dimension formulas for certain spaces of Drinfeld cusp forms

Gebhard Boeckle·Peter Mathias Graef·Iason Papadopoulos
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Abstract

In this short note, we derive dimension formulas for spaces of Drinfeld cusp forms corresponding to harmonic cocycles invariant under the group $\mathrm{SL}_2(\mathbb{F}_q[t])$ and with values in absolutely irreducible $\mathrm{SL}_2(\mathbb{F}_q(t))$-representations via the theory of Brauer characters. This generalizes results in [BGP21] obtained by different methods. In addition, we prove a simple asymptotic formula for these dimensions.

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BibTeXRIS

Gebhard Boeckle, Peter Mathias Graef, Iason Papadopoulos. 2025-02-24. Dimension formulas for certain spaces of Drinfeld cusp forms. https://arxiv.org/abs/2502.17582

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