# 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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