Elliptic curves, random matrices and orbital integrals
| Autor: | Achter, Jeff, Gordon, Julia, Altug, Salim Ali |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Pacific J. Math. 286 (2017) 1-24 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/pjm.2017.286.1 |
| Popis: | 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. Comment: Appendix by Salim Ali Altug. V3: Clarified Section 3.3 |
| Databáze: | arXiv |
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