Maximal Galois group of L-functions of elliptic curves

Autor:	Jouve, F.
Rok vydání:	2009
Předmět:	Mathematics - Number Theory 11N36 11G25 (Primary) 11E08 14D10 11C08 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0903.3898 Zobrazit plný text záznamu View this record from Arxiv