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 language | English |
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Pages (from-to) | 795-821 |
Number of pages | 27 |
Journal | Annals of Mathematics |
Volume | 199 |
Issue number | 2 |
DOIs | |
State | Published - Mar 2024 |
All Science Journal Classification (ASJC) codes
- Mathematics (miscellaneous)