Once more nice equations for nice groups

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.