论文标题
威尔基对Pfaffian结构的猜想
Wilkie's conjecture for Pfaffian structures
论文作者
论文摘要
我们证明了Wilkie在受限制的子Pfaffian函数产生的结构中的一种有效形式：该集合的先验部分中的理性高度点$ H $的理性点的增长速度不超过$ \ log H $的某些功率。我们的界限仅取决于所涉及的集合的PFAFFIAN复杂性。作为推论，我们将Wilkie的原始猜想推导为$ \ Mathbb {r} _ {\ Mathrm {exp}}} $以完整的通用性。
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 $\mathbb{R}_{\mathrm{exp}}$ in full generality.
