English

A closed form expression for the Drinfeld modular polynomial $\Phi_T(X,Y)$

Number Theory 2012-03-29 v1 Algebraic Geometry

Abstract

In this paper we give a closed form expression for the Drinfeld modular polynomial ΦT(X,Y)Fq(T)[X,Y]\Phi_T(X,Y) \in \mathbb{F}_q(T)[X,Y] for arbitrary qq and prove a conjecture of Schweizer. A new identity involving the Catalan numbers plays a central role.

Cite

@article{arxiv.1203.6288,
  title  = {A closed form expression for the Drinfeld modular polynomial $\Phi_T(X,Y)$},
  author = {Alp Bassa and Peter Beelen},
  journal= {arXiv preprint arXiv:1203.6288},
  year   = {2012}
}
R2 v1 2026-06-21T20:41:18.466Z