Maximal Galois group of L-functions of elliptic curves
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | JOUVE, Florent | |
| dc.date.accessioned | 2024-04-04T02:37:50Z | |
| dc.date.available | 2024-04-04T02:37:50Z | |
| dc.date.created | 2009-03-23 | |
| dc.date.issued | 2009-05-21 | |
| dc.identifier.issn | 1073-7928 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190834 | |
| dc.description.abstractEn | 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.language.iso | en | |
| dc.publisher | Oxford University Press (OUP) | |
| dc.title.en | Maximal Galois group of L-functions of elliptic curves | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1093/imrn/rnp066 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 0903.3898 | |
| bordeaux.journal | International Mathematics Research Notices | |
| bordeaux.page | ? | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00387291 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00387291v1 | |
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