Explicit formula of a supersingular polynomial for rank-2 Drinfeld modules and applications
arXiv:1701.07546
Abstract
Rank-2 Drinfeld modules are a function-field analogue of 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 of 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.
25 pages, Mistaken citations in Section 1 of an earlier version were corrected