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Monatshefte für Mathematik

, Volume 171, Issue 2, pp 241–253 | Cite as

Arithmetic properties of mirror maps associated with Gauss hypergeometric equations

  • Julien Roques
Article
  • 77 Downloads

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.

Keywords

Hypergeometric series and equations Mirror maps 

Mathematics Subject Classification (2000)

33C05 

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Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  1. 1.Institut FourierUniversité Grenoble 1, CNRS UMR 5582St Martin d’Hères cedexFrance

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