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arXiv · 1310.6158

Cubic polynomials represented by norm forms

A. J. Irving
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Abstract

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

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A. J. Irving. 2015-04-01. Cubic polynomials represented by norm forms. https://arxiv.org/abs/1310.6158

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