Goursat rigid local systems of rank four

@article{Radchenko2018GoursatRL,
  title={Goursat rigid local systems of rank four},
  author={Danylo V. Radchenko and Fernando Rodriguez Villegas},
  journal={Research in the Mathematical Sciences},
  year={2018},
  volume={5},
  pages={1-34}
}
We study the general properties of certain rank 4 rigid local systems considered by Goursat. We analyze when they are irreducible, give an explicit integral description as well as the invariant Hermitian form H when it exists. By a computer search, we find what we expect are all irreducible such systems all whose solutions are algebraic functions and give several explicit examples defined over $${\mathbb {Q}}$$Q. We also exhibit one example with infinite monodromy as arising from a family of… 

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