Quadratic polynomials represented by norm forms

Tim D Browning, DR Heath-Brown

Research output: Contribution to journalArticle (Academic Journal)peer-review

16 Citations (Scopus)


Let P(t)∈Q[t] be an irreducible quadratic polynomial and suppose that K is a quartic extension of Q containing the roots of P(t). Let N K/Q (x) be a full norm form for the extension K/Q . We show that the variety
P(t)=N K/Q (x)≠0
satisfies the Hasse principle and weak approximation. The proof uses analytic methods.
Original languageEnglish
Pages (from-to)1124-1190
Number of pages67
JournalGeometric and Functional Analysis
Issue number5
Publication statusPublished - Oct 2012


  • 14G05 (11D57, 14G25)


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