Arithmeticity of Certain Symplectic Hypergeometric Groups

Abstract

We give a sufficient condition on a pair of (primitive) integral polynomials that the associated hypergeometric group (monodromy group of the corresponding hypergeometric differential equation) is an arithmetic subgroup of the integral symplectic group.

31 pages, 4 tables (To appear in Duke Mathematical Journal)

References in corpus (1)

• Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds

Cited by in corpus (19)

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• Zariski Density and Computing in Arithmetic Groups
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• Generic Phenomena in Groups -- Some Answers and Many Questions
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• Generic thinness in finitely generated subgroups of ${\text{SL}}_n(\mathbb{Z})$
• Symplectic Hypergeometric Groups of Degree Six
• Thin monodromy in $\mathrm{Sp}(4)$ and $\mathrm{Sp}(6)$
• Counting roots of truncated hypergeometric series over finite fields
• Cones and ping-pong in three dimensions
• Orthogonal Hypergeometric Groups with a Maximally Unipotent Monodromy
• Commensurability and arithmetic equivalence for orthogonal hypergeometric monodromy groups