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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Once more nice equations for nice groups


Authors: Shreeram S. Abhyankar and Paul A. Loomis
Journal: Proc. Amer. Math. Soc. 126 (1998), 1885-1896
MSC (1991): Primary 12F10, 14H30, 20D06, 20E22
MathSciNet review: 1459101
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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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Additional Information

Shreeram S. Abhyankar
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: ram@cs.purdue.edu

Paul A. Loomis
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: loomisp@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04421-9
PII: S 0002-9939(98)04421-9
Received by editor(s): December 1, 1996
Additional Notes: The first author’s work was partly supported by NSA grant MDA 904-97-1-0010, and the second author’s work was partly supported by a PRF grant at Purdue University.
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1998 American Mathematical Society