p-adic properties of division polynomials and elliptic divisibility sequences
| dc.creator | Silverman, Joseph H. | |
| dc.date | 2004-04-22 | |
| dc.date.accessioned | 2026-07-07T08:14:25Z | |
| dc.date.available | 2026-07-07T08:14:25Z | |
| dc.description | For a given point P in the group of K-rational points E(K) of an elliptic curve, we consider the sequence of values (F_1(P),F_2(P),F_3(P),...) of the division polynomials of E at P. If K is a finite field, we prove that the sequence is periodic. If K/Q_p is a local field, we prove (under certain hypotheses) that there is a power q=p^e so that for all m > 0, the limit as k goes to infinity of F_{mq^{k}}(P) exists in K and is algebraic over Q(E). We apply this result to prove an analogous p-adic limit and algebraicity result for elliptic divisibility sequences. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404412 | |
| dc.identifier | http://arxiv.org/abs/math/0404412 | |
| dc.identifier | Math. Ann. 332 (2005), no. 2, 443--471, addendum 473-474. (MR2178070) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133113 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G07 (Primary); 11D61, 14G20, 14H52 (Secondary) | |
| dc.title | p-adic properties of division polynomials and elliptic divisibility sequences | |
| dc.type | text |