English

Dimension formulas for certain spaces of Drinfeld cusp forms

Number Theory 2025-02-26 v1

Abstract

In this short note, we derive dimension formulas for spaces of Drinfeld cusp forms corresponding to harmonic cocycles invariant under the group SL2(Fq[t])\mathrm{SL}_2(\mathbb{F}_q[t]) and with values in absolutely irreducible SL2(Fq(t))\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.

Keywords

Cite

@article{arxiv.2502.17582,
  title  = {Dimension formulas for certain spaces of Drinfeld cusp forms},
  author = {Gebhard Boeckle and Peter Mathias Graef and Iason Papadopoulos},
  journal= {arXiv preprint arXiv:2502.17582},
  year   = {2025}
}

Comments

15 pages

R2 v1 2026-06-28T21:56:10.723Z