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

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

2009-01-30

arxiv.org/abs/0901.4831v3

Mathematics

Number Theory

13 pages, 4 tables, to appear in Interdisciplinary Information Sciences

Scientific paper

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 $x^3-2mx^2y-9mxy^2-m(2m+27)y^3=\lambda$ where $\lambda^2$ is a
divisor of $m^3(4m+27)^5$.

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