Intégralité des coefficients de Taylor de racines d'applications miroir

Abstract

We prove the integrality of the Taylor coefficients of roots of mirror maps at the origin. By mirror maps, we mean formal power series z.exp(G(z)/F(z)), where F(z) and G(z)+log(z)F(z) are particular solutions of certain generalized hypergeometric differential equations. This enables us to prove a conjecture stated by Zhou in "Integrality properties of variations of Mahler measures" [arXiv:1006.2428v1 math.AG]. The proof of these results is an adaptation of the techniques used in our article "Critère pour l'intégralité des coefficients de Taylor des applications miroir", [J. Reine Angew. Math. (to appear)].