Algebraic Hypergeometric Functions
(Un exposé de Fernando Rodriguez-Villegas au séminaire de
théorie des nombres de Chevaleret le 13 décembre 2004)
Résumé :
I will discuss a characterization of the functions of the title
(classical one-variable hypergeometric series that satisfy a
polynomial equation) in terms of the integrality of its Taylor
coefficients. The proof follows the work of Beukers and Heckman and
relies on properties of the Hermitian form fixed by the monodromy
group. This Hermitian form, it turns out, can be described by an
ancient construction due to Bezout.