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

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.

47 pages; numerous minor changes

Cited by in corpus (5)

• Secondary terms in asymptotics for the number of zeros of quadratic forms over number fields
• On the Hasse principle for quartic hypersurfaces
• Forms of differing degrees over number fields
• Generalised quadratic forms over totally real number fields
• Metaplectic cusp forms and the large sieve