---
_id: '243'
abstract:
- lang: eng
text: 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.
author:
- first_name: Timothy D
full_name: Timothy Browning
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Roger
full_name: Heath-Brown, Roger
last_name: Heath Brown
citation:
ama: Browning TD, Heath Brown R. Quadratic polynomials represented by norm forms.
Geometric and Functional Analysis. 2012;22(5):1124-1190. doi:10.1007/s00039-012-0168-5
apa: Browning, T. D., & Heath Brown, R. (2012). Quadratic polynomials represented
by norm forms. Geometric and Functional Analysis. Springer Basel. https://doi.org/10.1007/s00039-012-0168-5
chicago: Browning, Timothy D, and Roger Heath Brown. “Quadratic Polynomials Represented
by Norm Forms.” Geometric and Functional Analysis. Springer Basel, 2012.
https://doi.org/10.1007/s00039-012-0168-5.
ieee: T. D. Browning and R. Heath Brown, “Quadratic polynomials represented by norm
forms,” Geometric and Functional Analysis, vol. 22, no. 5. Springer Basel,
pp. 1124–1190, 2012.
ista: Browning TD, Heath Brown R. 2012. Quadratic polynomials represented by norm
forms. Geometric and Functional Analysis. 22(5), 1124–1190.
mla: Browning, Timothy D., and Roger Heath Brown. “Quadratic Polynomials Represented
by Norm Forms.” Geometric and Functional Analysis, vol. 22, no. 5, Springer
Basel, 2012, pp. 1124–90, doi:10.1007/s00039-012-0168-5.
short: T.D. Browning, R. Heath Brown, Geometric and Functional Analysis 22 (2012)
1124–1190.
date_created: 2018-12-11T11:45:24Z
date_published: 2012-08-25T00:00:00Z
date_updated: 2021-01-12T06:57:26Z
day: '25'
doi: 10.1007/s00039-012-0168-5
extern: 1
intvolume: ' 22'
issue: '5'
month: '08'
page: 1124 - 1190
publication: Geometric and Functional Analysis
publication_status: published
publisher: Springer Basel
publist_id: '7661'
quality_controlled: 0
status: public
title: Quadratic polynomials represented by norm forms
type: journal_article
volume: 22
year: '2012'
...