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On generalized hypergeometric equations and mirror maps


Author: Julien Roques
Journal: Proc. Amer. Math. Soc. 142 (2014), 3153-3167
MSC (2010): Primary 33C20
DOI: https://doi.org/10.1090/S0002-9939-2014-12161-7
Published electronically: May 28, 2014
MathSciNet review: 3223372
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Abstract: This paper deals with generalized hypergeometric differential
equations of order $ n \geq 3$ having maximal unipotent monodromy at 0. We show that among these equations those leading to mirror maps with integral Taylor coefficients at 0 (up to simple rescaling) have special parameters, namely $ R$-partitioned parameters. This result yields the classification of all generalized hypergeometric differential equations of order $ n \geq 3$ having maximal unipotent monodromy at 0 such that the associated mirror map has the above integrality property.


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Additional Information

Julien Roques
Affiliation: Université Grenoble Alpes, Institut Fourier, CNRS UMR 5582, 100 rue des Maths, BP 74, 38402 St. Martin d’Hères, France
Email: Julien.Roques@ujf-grenoble.fr

DOI: https://doi.org/10.1090/S0002-9939-2014-12161-7
Keywords: Generalized hypergeometric series and equations, mirror maps
Received by editor(s): June 22, 2012
Received by editor(s) in revised form: October 2, 2012
Published electronically: May 28, 2014
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.