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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.17582 |
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| _version_ | 1866917935577038848 |
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| author | Boeckle, Gebhard Graef, Peter Mathias Papadopoulos, Iason |
| author_facet | Boeckle, Gebhard Graef, Peter Mathias Papadopoulos, Iason |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17582 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimension formulas for certain spaces of Drinfeld cusp forms Boeckle, Gebhard Graef, Peter Mathias Papadopoulos, Iason Number Theory 11F52 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. |
| title | Dimension formulas for certain spaces of Drinfeld cusp forms |
| topic | Number Theory 11F52 |
| url | https://arxiv.org/abs/2502.17582 |