The sign of an elliptic divisibility sequence
| dc.creator | Silverman, Joseph H. | |
| dc.creator | Stephens, Nelson | |
| dc.date | 2004-02-25 | |
| dc.date.accessioned | 2026-07-07T08:14:24Z | |
| dc.date.available | 2026-07-07T08:14:24Z | |
| dc.description | An elliptic divisibility sequence (EDS) is a sequence of integers W_0,W_1,W_2,... generated by the nonlinear recursion satisfied by the division polyomials of an elliptic curve. We give a formula for the sign of W_n for unbounded nonsingular elliptic divisibility sequences. A typical case is Sign(W_n) = (-1)^[n*b] for an irrational real number b, where [x] denotes the greatest integer in x. As an application, we show that the associated sequence of absolute values |W_1|,|W_2|,|W_3|,... cannot be realized as the sequence counting fixed points of any (abstract) dynamical system. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0402415 | |
| dc.identifier | http://arxiv.org/abs/math/0402415 | |
| dc.identifier | J. Ramanujan Math. Soc. 21 (2006), no. 1, 1--17.(MR2226354) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133112 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11D61 (Primary) 11G35 (Secondary) | |
| dc.title | The sign of an elliptic divisibility sequence | |
| dc.type | text |