Abstract
We draw up the list of Gauss hypergeometric differential equations having maximal unipotent monodromy at \(0\) whose associated mirror map has, up to a simple rescaling, integral Taylor coefficients at \(0\). We also prove that these equations are characterized by much weaker integrality properties (of \(p\)-adic integrality for infinitely many primes \(p\) in suitable arithmetic progressions). It turns out that the mirror maps with the above integrality property have modular origins.
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Communicated by C. Krattenthaler.
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Roques, J. Arithmetic properties of mirror maps associated with Gauss hypergeometric equations. Monatsh Math 171, 241–253 (2013). https://doi.org/10.1007/s00605-013-0505-2
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DOI: https://doi.org/10.1007/s00605-013-0505-2