Quadratic polynomials represented by norm forms

T.D. Browning, R. Heath Brown, Geometric and Functional Analysis 22 (2012) 1124–1190.

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Abstract
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.
Publishing Year
Date Published
2012-08-25
Journal Title
Geometric and Functional Analysis
Volume
22
Issue
5
Page
1124 - 1190
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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
Browning, T. D., & Heath Brown, R. (2012). Quadratic polynomials represented by norm forms. Geometric and Functional Analysis, 22(5), 1124–1190. https://doi.org/10.1007/s00039-012-0168-5
Browning, Timothy D, and Roger Heath Brown. “Quadratic Polynomials Represented by Norm Forms.” Geometric and Functional Analysis 22, no. 5 (2012): 1124–90. https://doi.org/10.1007/s00039-012-0168-5.
T. D. Browning and R. Heath Brown, “Quadratic polynomials represented by norm forms,” Geometric and Functional Analysis, vol. 22, no. 5, pp. 1124–1190, 2012.
Browning TD, Heath Brown R. 2012. Quadratic polynomials represented by norm forms. Geometric and Functional Analysis. 22(5), 1124–1190.
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.

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