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arXiv · 2605.25935

Certifying Arithmeticity for Two Degree-Six Symplectic Hypergeometric Monodromy Groups

J. Maxwell Riestenberg·Diaaeldin Taha·Steve Trettel·Anna Wienhard
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Abstract

We prove arithmeticity for two degree-six symplectic hypergeometric monodromy groups, called C-47, and C-55 in the paper \cite{BajpaiDonaNitsche2025Thin} by Bajpai-Dona-Nitsche. This settles two of the three remaining cases, whose classification was left open by \cite{BajpaiDonaNitsche2025Thin}. The arithmeticity certificates were found with AlphaEvolve and then independently verified with exact matrix arithmetic over $\QQ$ using a computer. We include illustrations of limit sets of several degree-six symplectic hypergeometric monodromy groups. Based on these illustration we conjecture C-32 to be thin.

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J. Maxwell Riestenberg, Diaaeldin Taha, Steve Trettel, Anna Wienhard. 2026-05-25. Certifying Arithmeticity for Two Degree-Six Symplectic Hypergeometric Monodromy Groups. https://arxiv.org/abs/2605.25935

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