Arithmetic of quadratic fields and torsion in Jacobians (Q606500)

Let \(K\) be an algebraic number field, \(f(x)=x^{2n}+a_{2n-1}x^{2n-1}+\ldots+a_0\in K[X]\) a squarefree polynomial, \[ D_f=K[X](\sqrt{f})=\{\alpha+\beta\sqrt{f}\mid \alpha,\beta\in K[X]\}. \] The author formulates a local-global principle for the existence of nontrivial units in \(D_f\).