Tobias Hilgart

Complete Resolution Of A Family Of Twisted Thue Equations

One of the first infinite families of Thue equations, $$F_n(X)=X^3 - (n-1) X^2Y - (n+2)XY^2 - Y^3 = \pm 1$$ for $n\in \mathbb{Z}$, was solved by Thomas in 1990. This family is associated to the simplest cubic fields $\mathbb{Q}(\lambda)$ of Shanks, where $\lambda$ is a root of $F_n(X,1)$. Levesque and Waldschmidt twist...