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.
Acknowledgments
We thank Professor Martin Kassabov for his helpful advice. Many thanks are due also to our referees, whose comments led to improvements of the paper. We are grateful to Mathematisches Forschungsinstitut Oberwolfach and the Hausdorff Research Institute for Mathematics for hospitality and facilitation of our work during visits in 2018.
Declaration of interest
No potential conflict of interest was reported by the author(s).