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

T. D. Browning; P. Vishe

doi:10.1215/00127094-2738530

Abstract

A version of the Hardy–Littlewood circle method is developed for number fields $K/\mathbb {Q}$ and is used to show that nonsingular projective cubic hypersurfaces over $K$ always have a $K$ -rational point when they have dimension at least $8$ .

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T. D. Browning. P. Vishe. "Cubic hypersurfaces and a version of the circle method for number fields." Duke Math. J. 163 (10) 1825 - 1883, 15 July 2014. https://doi.org/10.1215/00127094-2738530

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Published: 15 July 2014

First available in Project Euclid: 8 July 2014

zbMATH: 1298.11098

MathSciNet: MR3229043

Digital Object Identifier: 10.1215/00127094-2738530

Subjects:

Primary: 11P55

Secondary: 11D72 , 14G05

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