Cubic hypersurfaces and a version of the circle method for number fields

T.D. Browning, P. Vishe, Duke Mathematical Journal 163 (2014) 1825–1883.

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Journal Article | Published
Author
Abstract
A version of the Hardy-Littlewood circle method is developed for number fields K/ℚ and is used to show that nonsingular projective cubic hypersurfaces over K always have a K-rational point when they have dimension at least 8.
Publishing Year
Date Published
2014-07-01
Journal Title
Duke Mathematical Journal
Volume
163
Issue
10
Page
1825 - 1883
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Browning TD, Vishe P. Cubic hypersurfaces and a version of the circle method for number fields. Duke Mathematical Journal. 2014;163(10):1825-1883. doi:10.1215/00127094-2738530
Browning, T. D., & Vishe, P. (2014). Cubic hypersurfaces and a version of the circle method for number fields. Duke Mathematical Journal, 163(10), 1825–1883. https://doi.org/10.1215/00127094-2738530
Browning, Timothy D, and Pankaj Vishe. “Cubic Hypersurfaces and a Version of the Circle Method for Number Fields.” Duke Mathematical Journal 163, no. 10 (2014): 1825–83. https://doi.org/10.1215/00127094-2738530.
T. D. Browning and P. Vishe, “Cubic hypersurfaces and a version of the circle method for number fields,” Duke Mathematical Journal, vol. 163, no. 10, pp. 1825–1883, 2014.
Browning TD, Vishe P. 2014. Cubic hypersurfaces and a version of the circle method for number fields. Duke Mathematical Journal. 163(10), 1825–1883.
Browning, Timothy D., and Pankaj Vishe. “Cubic Hypersurfaces and a Version of the Circle Method for Number Fields.” Duke Mathematical Journal, vol. 163, no. 10, Duke University Press, 2014, pp. 1825–83, doi:10.1215/00127094-2738530.

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