Combinatorial Aspects of Elliptic Curves
| dc.creator | Musiker, Gregg | |
| dc.date | 2007-07-23 | |
| dc.date.accessioned | 2026-07-07T08:19:35Z | |
| dc.date.available | 2026-07-07T08:19:35Z | |
| dc.description | Given an elliptic curve C, we study here $N_k = #C(F_{q^k})$, the number of points of C over the finite field F_{q^k}. This sequence of numbers, as k runs over positive integers, has numerous remarkable properties of a combinatorial flavor in addition to the usual number theoretical interpretations. In particular we prove that $N_k = - W_k(q, - N_1)$ where W_k(q,t) is a (q,t)-analogue of the number of spanning trees of the wheel graph. Additionally we develop a determinantal formula for N_k where the eigenvalues can be explicitly written in terms of q, N_1, and roots of unity. We also discuss here a new sequence of bivariate polynomials related to the factorization of N_k, which we refer to as elliptic cyclotomic polynomials because of their various properties. | |
| dc.description | 29 pages, Section 2 presented at FPSAC 2006 | |
| dc.identifier | https://arxiv.org/abs/0707.3179 | |
| dc.identifier | http://arxiv.org/abs/0707.3179 | |
| dc.identifier | Seminaire Lotharingien de Combinatoire, vol. 56 (2007) Art. B56f | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134811 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.title | Combinatorial Aspects of Elliptic Curves | |
| dc.type | text |