Interdisciplinary Information Sciences
Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050
Special Section: Japan-Korea Joint Seminar on Number Theory and Related Topics 2008
A Note on the Field Isomorphism Problem of X3+sX+s and Related Cubic Thue Equations
Akinari HOSHIKatsuya MIYAKE
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2010 Volume 16 Issue 1 Pages 45-54

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Abstract

We study the field isomorphism problem of cubic generic polynomial X3+sX+s over the field of rational numbers with the specialization of the parameter s to nonzero rational integers m via primitive solutions to the family of cubic Thue equations x3−2mx2y−9mxy2m(2m+27)y3=λ where λ2 is a divisor of m3(4m+27)5.

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© 2010 by the Graduate School of Information Sciences (GSIS), Tohoku University

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