Forms in many variables and differing degrees

Tim Browning, Roger Heath-Brown

Research output: Contribution to journalArticle (Academic Journal)peer-review

23 Citations (Scopus)
257 Downloads (Pure)


We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin-Peyre conjecture for a smooth and geometrically integral variety X Pm, provided only that its dimension is large enough in terms of its degree.

Original languageEnglish
Pages (from-to)357-394
Number of pages38
JournalJournal of the European Mathematical Society
Issue number2
Publication statusPublished - 26 Jan 2017


  • Complete intersections
  • Forms in many variables
  • Hardy-Littlewood circle method
  • Hasse principle
  • Rational points Manin conjecture
  • Weak approximation


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