Galois Groups Via Atkin-Lehner Twists
| dc.creator | Clark, Pete L. | |
| dc.date | 2005-06-23 | |
| dc.date | 2005-09-09 | |
| dc.date.accessioned | 2026-07-07T05:21:07Z | |
| dc.date.available | 2026-07-07T05:21:07Z | |
| dc.description | Using Serre's proposed complement to Shih's Theorem, we obtain PSL_2(F_p) as a Galois group over Q for at least 614 new primes p. Under the assumption that rational elliptic curves with odd analytic rank have positive rank, we obtain Galois realizations for 3/8 of the primes not covered by previous results; it would also suffice to assume a certain (plausible, and perhaps tractable) conjecture concerning class numbers of quadratic fields. The key issue is to understand rational points on Atkin-Lehner twists of X_0(N). In an appendix, we explore the existence of local points on these curves. | |
| dc.description | An "appendix" has been added containing additional results. There are many minor expository changes. 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0506490 | |
| dc.identifier | http://arxiv.org/abs/math/0506490 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75574 | |
| dc.subject | Number Theory | |
| dc.title | Galois Groups Via Atkin-Lehner Twists | |
| dc.type | text |