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On Congruences Between Drinfeld Modular Forms

Arash Rastegar
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Abstract

Let ${\mathbf F}_q$ denote a finite field of characteristic $p$ and let $n$ be an effective divisor on the affine line over ${\mathbf F}_q$ and let $v$ be a point on the affine line outside $n$. In this paper, we get congruences between ${\mathbb Q}_l$-valued weight two $v$-old Drinfeld modular forms and $v$-new Drinfeld modular forms of level $vn$. In order to do this, we shall first construct a cokernel torsion-free injection from a full lattice in the space of $v$-old Drinfeld modular forms of level $vn$ into a full lattice in the space of all Drinfeld modular forms of level $vn$. To get this injection we use ideas introduced by Gekeler and Reversat on uniformization of jacobians of Drinfeld moduli curves.

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Arash Rastegar. 2004-05-27. On Congruences Between Drinfeld Modular Forms. https://arxiv.org/abs/math/0405518

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