Elliptic curves, random matrices and orbital integrals
Number Theory
2016-12-14 v3
Abstract
An isogeny class of elliptic curves over a finite field is determined by a quadratic Weil polynomial. Gekeler has given a product formula, in terms of congruence considerations involving that polynomial, for the size of such an isogeny class. In this paper, we give a new, transparent proof of this formula; it turns out that this product actually computes an adelic orbital integral which visibly counts the desired cardinality. This answers a question posed by N. Katz.
Cite
@article{arxiv.1510.07068,
title = {Elliptic curves, random matrices and orbital integrals},
author = {Jeff Achter and Julia Gordon and Salim Ali Altug},
journal= {arXiv preprint arXiv:1510.07068},
year = {2016}
}
Comments
Appendix by Salim Ali Altug. V3: Clarified Section 3.3