Simplest Cubic Fields
By Franz Lemmermeyer, Attila Pethö. 2010
77 citations recorded by the source corpus.
Let $Q(\alpha)$ be the simplest cubic field, it is known that $Q(\alpha)$ can be generated by adjoining a root of the irreducible equation $x^{3}-kx^{2}+(k-3)x+1=0$, where $k$ belongs to $Q$. In this paper we have established a relationship between $\alpha$, $\alpha'$ and $k,k'$ where $\alpha$ is a root of the equation $x^{3}-kx^{2}+(k-3)x+1=0$ and $\alpha'$ is a root of the same equation with $k$ replaced by $k'$ and $Q(\alpha)=Q(\alpha')$.
Subfields: Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/431e4726249fa96eb434269374dba3c5f0b58bd6
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In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- Class Field Towers (2010, methodology): “We start with the following proposition, which can be proved by the method discussed by Lemmermeyer and Pethö [116]: Proposition 1.5.2.”