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On the Deuring polynomial for Drinfeld modules in Legendre form

Volume 186 / 2018

Alp Bassa, Peter Beelen Acta Arithmetica 186 (2018), 179-190 MSC: Primary 11G09, 11F52, 11R58; Secondary 11G18, 14G35. DOI: 10.4064/aa170707-17-2 Published online: 20 September 2018

Abstract

We study a family $\psi^{\lambda}$ of $\mathbb F_q[T]$-Drinfeld modules, which is a natural analog of Legendre elliptic curves. We then find a surprising recurrence giving the corresponding Deuring polynomial $H_{p(T)}(\lambda)$ characterising supersingular Legendre Drinfeld modules $\psi^{\lambda}$ in characteristic $p(T)$.

Authors

  • Alp BassaDepartment of Mathematics
    Faculty of Arts and Sciences
    Boğaziçi University
    34342 Bebek, İstanbul, Turkey
    e-mail
  • Peter BeelenDepartment of Applied Mathematics and Computer Science
    Technical University of Denmark
    Matematiktorvet 303B
    2800 Kongens Lyngby, Denmark
    e-mail

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