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arXiv · 0901.4831

A note on the field isomorphism problem of X^3+sX+s and related cubic Thue equations

Akinari Hoshi·Katsuya Miyake
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Abstract

We study the field isomorphism problem of cubic generic polynomial $X^3+sX+s$ 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 $x^3-2mx^2y-9mxy^2-m(2m+27)y^3=λ$ where $λ^2$ is a divisor of $m^3(4m+27)^5$.

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Akinari Hoshi, Katsuya Miyake. 2009-07-14. A note on the field isomorphism problem of X^3+sX+s and related cubic Thue equations. https://arxiv.org/abs/0901.4831

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