On the Deuring polynomial for Drinfeld modules in Legendre form
Volume 186 / 2018
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 $p(T)$.
