Ordinary elliptic curves of high rank over $\bar F_p(x)$ with constant j-invariant
| dc.creator | Bouw, Irene I. | |
| dc.creator | Diem, Claus | |
| dc.creator | Scholten, Jasper | |
| dc.date | 2003-05-04 | |
| dc.date.accessioned | 2026-07-07T04:57:45Z | |
| dc.date.available | 2026-07-07T04:57:45Z | |
| dc.description | We show that under the assumption of Artin's Primitive Root Conjecture, for all primes p there exist ordinary elliptic curves over $\bar F_p(x)$ with arbitrary high rank and constant j-invariant. For odd primes p, this result follows from a theorem which states that whenever p is a generator of (Z/ell Z)^*/<-1> (ell an odd prime) there exists a hyperelliptic curve over $\bar F_p$ whose Jacobian is isogenous to a power of one ordinary elliptic curve. | |
| dc.description | 15 pages, 0 figures, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0305064 | |
| dc.identifier | http://arxiv.org/abs/math/0305064 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67366 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G05 (Primary); 11G20; 14H40; 14H52 (Secondary) | |
| dc.title | Ordinary elliptic curves of high rank over $\bar F_p(x)$ with constant j-invariant | |
| dc.type | text |