Heights and morphisms in number fields

2024/11/20 by Matt Olechnowicz, Olechnowicz, Matt
Computer Science · Mathematics · #Advanced Mathematical Theories #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2411.13522

openalex publication_date 2024/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a formula with explicit error term for the number of K-rational points P satisfying H(f(P)) ≤ X as X → ∞, where f is a nonconstant morphism between projective spaces defined over a number field K and H is the absolute multiplicative Weil height. This yields formulae for the counting functions of f(ℙ^m(K)) with respect to the Weil height as well as of ℙ^m(K) with respect to the Call-Silverman canonical height.

Related

• Rational points of bounded height and the Weil restriction
• Counting rational points on weighted projective spaces over number fields
• Schanuel's theorem for heights defined via extension fields
• Rational Points on Weighted projective Spaces
• Variation of the canonical height for polynomials in several variables