Explicit formula of a supersingular polynomial for rank-2 Drinfeld modules and applications

Takehiro Hasegawa

Published 2017-01-26Version 1

Rank-2 Drinfeld modules are a function-field analogue of the elliptic curves, and the purpose of this paper is to investigate similarities and differences between rank-2 Drinfeld modules and elliptic curves in terms of supersingularity. Specifically, we provide an explicit formula for a supersingular polynomial for rank-2 Drinfeld modules and prove several basic properties. As an application, we give a numerical example of an asymptotically optimal tower of Drinfeld modular curves.