Quadratic polynomials represented by norm forms

2011/09/01 by Browning, T. D., Heath-Brown, D. R.
#14G05 (11D57 #14G25) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1109.0232

Abstract

The Hasse principle and weak approximation is established for equations of the shape P(t)=N(x₁,x₂,x₃,x₄), where P is an irreducible quadratic polynomial in one variable and N is a norm form associated to a quartic extension of the rationals containing the roots of P. The proof uses analytic methods.

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