Wilkie’s conjecture for Pfaffian structures

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Abstract

We prove an effective form of Wilkie’s conjecture in the structure generated by restricted sub-Pfaffian functions: the number of rational points of height H lying in the transcendental part of such a set grows no faster than some power of log H. Our bounds depend only on the Pfaffian complexity of the sets involved. As a corollary we deduce Wilkie’s original conjecture for Rexp in full generality.

Original languageEnglish
Pages (from-to)795-821
Number of pages27
JournalAnnals of Mathematics
Volume199
Issue number2
DOIs
StatePublished - Mar 2024

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

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