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

Published 10 Jul 2012 in math.NT | (1207.2385v2)

Abstract: A version of the Hardy-Littlewood circle method is developed for number fields K/Q and is used to show that non-singular projective cubic hypersurfaces over K always have a K-rational point when they have dimension at least 8.

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