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Integrality of the Taylor coefficients of roots of mirror maps. (Intégralité des coefficients de Taylor de racines d’applications miroir.) (French. English summary) Zbl 1297.11072
Summary: We demonstrate the integrality of the Taylor coefficients of roots of formal power series \(q(z):=z \exp(G(z)/F(z))\), where \(F(z)\) and \(G(z)+\log(z)F(z)\) are particular solutions of certain hypergeometric differential equations. This allows us to prove a conjecture stated by J. Zhou [“Integrality properties of variations of Mahler measures”, http://arxiv.org/abs/1006.2428]. The proof of these results is an adaptation of the techniques used in the author’s article [J. Reine Angew. Math. 662, 205–252 (2012; Zbl 1271.11066)].

MSC:
11G42 Arithmetic mirror symmetry
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