--- _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' ...