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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.

##### MSC:
 33C05 Classical hypergeometric functions, $${}_2F_1$$
##### Keywords:
hypergeometric series and equations; mirror maps
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##### References:
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