Cubic polynomials represented by norm forms

2013/10/23 by Irving, A. J. · 1 citation
#11D57 #11N36 #14G05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1310.6158

Abstract

We show that for an irreducible cubic f∈\mathbb Z[x] and a full norm form \mathbf N(x₁,…,x_k) for a number field K/\mathbb Q satisfying certain hypotheses the variety f(t)=\mathbf N(x₁,…,x_k)≠ 0 satisfies the Hasse principle. Our proof uses sieve methods.

Cited by

• Cubic polynomials and sums of two squares

Related

• Polynomials represented by norm forms via the beta sieve
• Norm forms for arbitrary number fields as products of linear polynomials
• Quadratic polynomials represented by norm forms
• A positive proportion of plane cubics fail the Hasse principle
• Universal torsors and values of quadratic polynomials represented by norms