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

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

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

References in corpus (3)

• On the field intersection problem of generic polynomials: a survey
• On the field intersection problem of quartic generic polynomials via formal Tschirnhausen transformation
• On the field intersection problem of solvable quintic generic polynomials