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

Tim Browning, Pankaj Vishe

Research output: Working paperPreprint


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.
Original languageEnglish
PublisherArxiv (Cornell University)
Number of pages45
Publication statusAccepted/In press - 10 Jul 2012


  • math.NT
  • 11P55 (Primary)
  • 11D72
  • 14G05 (Secondary)

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