English

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

Number Theory 2017-05-15 v2 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.1701.07546,
  title  = {Explicit formula of a supersingular polynomial for rank-2 Drinfeld modules and applications},
  author = {Takehiro Hasegawa},
  journal= {arXiv preprint arXiv:1701.07546},
  year   = {2017}
}

Comments

25 pages, Mistaken citations in Section 1 of an earlier version were corrected