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Arithmetic properties of mirror maps associated with Gauss hypergeometric equations. (English) Zbl 1314.33005
A catalog of hypergeometric differential equations is constructed with maximal unipotent monodromy at the origin whose mirror map has integral Taylor coefficients up to a rescaling. For infinitely many primes \(p\) in certain arithmetic progressions, the mirror maps are shown to exhibit \(p\)-adic integrality. Mirror maps with the above properties are parameterized by modular functions.

33C05 Classical hypergeometric functions, \({}_2F_1\)
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