Int\'egralit\'e des coefficients de Taylor de racines d'applications miroir
Number Theory
2015-10-26 v1 Algebraic Geometry
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 "Crit\`ere pour l'int\'egralit\'e des coefficients de Taylor des applications miroir", [J. Reine Angew. Math. (to appear)].
Cite
@article{arxiv.1012.2331,
title = {Int\'egralit\'e des coefficients de Taylor de racines d'applications miroir},
author = {Eric Delaygue},
journal= {arXiv preprint arXiv:1012.2331},
year = {2015}
}