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

Akinari Hoshi; Katsuya Miyake

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

Number Theory 2009-07-14 v3

Authors: Akinari Hoshi , Katsuya Miyake

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

Keywords

field isomorphism problem cubic generic polynomial Thue equation rational integers primitive solutions

Cite

@article{arxiv.0901.4831,
  title  = {A note on the field isomorphism problem of X^3+sX+s and related cubic Thue equations},
  author = {Akinari Hoshi and Katsuya Miyake},
  journal= {arXiv preprint arXiv:0901.4831},
  year   = {2009}
}

Comments

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

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

Abstract

Keywords

Cite

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