Cubic hypersurfaces and a version of the circle method for number fields
(2014)
Journal Article
Browning, T., & 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
A version of the Hardy–Littlewood circle method is developed for number fields K/QK/Q and is used to show that nonsingular projective cubic hypersurfaces over KK always have a KK-rational point when they have dimension at least 88.