Abstract

We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results are obtained by extending our earlier algorithms for Zariski dense groups, based on the strong approximation and congruence subgroup properties.

中文翻译：

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辛超几何单值群实验

摘要

我们提出了超几何微分方程的辛单值群的新计算结果。特别是，我们计算每个组的算术闭包，有时证明算术性。结果是通过基于强近似和同余子群属性扩展我们早期的 Zariski 稠密群算法获得的。