Cubic polynomials represented by norm forms

Abstract

We show that for an irreducible cubic $f\in \mathbb{Z}[x]$ and a full norm form $\mathbf{N}(x_1,\dots ,x_k)$ for a number field $K/\mathbb{Q}$ satisfying certain hypotheses the variety $f(t)=\mathbf{N}(x_1,\dots ,x_k)\ne 0$ satisfies the Hasse principle. Our proof uses sieve methods.

40 pages, V2 contains some Minor corrections, V3 includes the bibliography which was missing in V2

References in corpus (1)

• Universal torsors and values of quadratic polynomials represented by norms