Effective Pila--Wilkie bounds for unrestricted Pfaffian surfaces

Gareth Jones, Margaret Thomas

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We prove effective Pila--Wilkie estimates for the number of rational points of bounded height lying on certain surfaces defined by Pfaan
functions. The class of surfaces to which our result applies includes, for instance, graphs of unrestricted Pfaan functions defined on the plane.
Original languageEnglish
Pages (from-to)0
JournalMathematische Annalen
Publication statusPublished - 25 Jul 2020


  • Pfaffian functions
  • effectivity
  • rational points
  • the Pila--Wilkie Theorem


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