{"_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."}],"status":"public","publisher":"Springer Basel","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","first_name":"Timothy D","full_name":"Timothy Browning","last_name":"Browning"},{"first_name":"Roger","last_name":"Heath Brown","full_name":"Heath-Brown, Roger"}],"publication":"Geometric and Functional Analysis","type":"journal_article","extern":1,"page":"1124 - 1190","day":"25","volume":22,"year":"2012","title":"Quadratic polynomials represented by norm forms","issue":"5","date_created":"2018-12-11T11:45:24Z","date_updated":"2021-01-12T06:57:26Z","intvolume":"        22","date_published":"2012-08-25T00:00:00Z","publication_status":"published","month":"08","citation":{"apa":"Browning, T. D., &#38; Heath Brown, R. (2012). Quadratic polynomials represented by norm forms. <i>Geometric and Functional Analysis</i>. Springer Basel. <a href=\"https://doi.org/10.1007/s00039-012-0168-5\">https://doi.org/10.1007/s00039-012-0168-5</a>","short":"T.D. Browning, R. Heath Brown, Geometric and Functional Analysis 22 (2012) 1124–1190.","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.” <i>Geometric and Functional Analysis</i>, vol. 22, no. 5, Springer Basel, 2012, pp. 1124–90, doi:<a href=\"https://doi.org/10.1007/s00039-012-0168-5\">10.1007/s00039-012-0168-5</a>.","chicago":"Browning, Timothy D, and Roger Heath Brown. “Quadratic Polynomials Represented by Norm Forms.” <i>Geometric and Functional Analysis</i>. Springer Basel, 2012. <a href=\"https://doi.org/10.1007/s00039-012-0168-5\">https://doi.org/10.1007/s00039-012-0168-5</a>.","ieee":"T. D. Browning and R. Heath Brown, “Quadratic polynomials represented by norm forms,” <i>Geometric and Functional Analysis</i>, vol. 22, no. 5. Springer Basel, pp. 1124–1190, 2012.","ama":"Browning TD, Heath Brown R. Quadratic polynomials represented by norm forms. <i>Geometric and Functional Analysis</i>. 2012;22(5):1124-1190. doi:<a href=\"https://doi.org/10.1007/s00039-012-0168-5\">10.1007/s00039-012-0168-5</a>"},"doi":"10.1007/s00039-012-0168-5","publist_id":"7661","quality_controlled":0}