Wilkie's conjecture for Pfaffian structures

2022/02/10 by Gal Binyamini, Binyamini, Gal, Dmitry A. Novikov +3 · 3 citations
Computer Science · Mathematics · #11U09 #14P10 #Algebraic Geometry (math.AG) #FOS: Mathematics #Limits and Structures in Graph Theory #Logic (math.LO) #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Primary 03C64 #Secondary 11G50 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2202.05305

openalex publication_date 2022/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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 ℝ_exp in full generality.

Cited by

• Additive relations in irrational powers
• Counting rational points on transcendental curves in valued fields
• Bounds for rational points on algebraic curves, optimal in the degree, and dimension growth

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