The two variable generating function of Hecke L-values
of CM elliptic curves
(Un exposé de Shinichi Kobayashi au séminaire de
théorie des nombres de Chevaleret le 18 octobre 2004)
Résumé :
Generating functions are important to construct p-adic L-functions.
Especially, at good supersingular primes for CM elliptic curves,
it would be worthwhile to study the two variable generating function
of Hecke L-values, since in this case the p-adic L-function of "two
variable"
has not yet constructed.
In this talk I will give an algebraic characterization of the two variable
generating function of Hecke L-values of CM elliptic curves as
a theta function corresponding to a section of the Poincar\'e bundle.
At good ordinary primes, I will show a simple construction of
the two variable p-adic L-function using this characterization.
At good supersingular primes,
I will give a p-adic estimate of the denominators of the coefficients
of the generating function.