Once more nice equations for nice groups

Abhyankar, Shreeram; Loomis, Paul

doi:10.1090/S0002-9939-98-04421-9

Once more nice equations for nice groups
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by Shreeram S. Abhyankar and Paul A. Loomis PDF

Proc. Amer. Math. Soc. 126 (1998), 1885-1896 Request permission

Abstract:

In a previous paper, nice quintinomial equations were given for unramified coverings of the affine line in nonzero characteristic $p$ with the projective symplectic isometry group PSp$(2m,q)$ and the (vectorial) symplectic isometry group Sp$(2m,q)$ as Galois groups where $m>2$ is any integer and $q>1$ is any power of $p$. Here we deform these equations to get nice quintinomial equations for unramified coverings of the once punctured affine line in characteristic $p$ with the projective symplectic similitude group PGSp$(2m,q)$ and the (vectorial) symplectic similitude group GSp$(2m,q)$ as Galois groups.

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