Maximal Galois group of L-functions of elliptic curves
| dc.creator | Jouve, F. | |
| dc.date | 2009-03-23 | |
| dc.date.accessioned | 2026-07-07T12:55:43Z | |
| dc.date.available | 2026-07-07T12:55:43Z | |
| dc.description | We give a quantitative version of a result due to N. Katz about L-functions of elliptic curves over function fields over finite fields. Roughly speaking, Katz's Theorem states that, on average over a suitably chosen algebraic family, the L-function of an elliptic curve over a function field becomes "as irreducible as possible" when seen as a polynomial with rational coefficients, as the cardinality of the field of constants grows. A quantitative refinement is obtained as a corollary of our main result which gives an estimate for the proportion of elliptic curves studied whose L-functions have "maximal" Galois group . To do so we make use of E. Kowalski's idea to apply large sieve methods in algebro-geometric contexts. Besides large sieve techniques, we use results of C. Hall on finite orthogonal monodromy and previous work of the author on orthogonal groups over finite fields. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/0903.3898 | |
| dc.identifier | http://arxiv.org/abs/0903.3898 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224345 | |
| dc.subject | Number Theory | |
| dc.subject | 11N36, 11G25 (Primary); 11E08, 14D10, 11C08 (Secondary) | |
| dc.title | Maximal Galois group of L-functions of elliptic curves | |
| dc.type | text |