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Archiv der Mathematik

, Volume 99, Issue 3, pp 237–245 | Cite as

A closed-form expression for the Drinfeld modular polynomial Φ T (X, Y)

  • Alp Bassa
  • Peter Beelen
Article
  • 114 Downloads

Abstract

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

Mathematics Subject Classification (2010)

Primary 11F32 11F52 05A10 11B65 Secondary 11G09 14G35 11F03 

Keywords

Drinfeld modular polynomial Catalan numbers Drinfeldmodular curves 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Sabancı University, MDBFTuzla, IstanbulTurkey
  2. 2.Department of MathematicsTechnical University of DenmarkLyngbyDenmark

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