Counting rational points on weighted projective spaces over number fields
Preprint
Abstract
Deng (arXiv:math/9812082) gave an asymptotic formula for the number of rational points on a weighted projective space over a number field with respect to a certain height function. We prove a generalization of Deng's result involving a morphism between weighted projective spaces, allowing us to count rational points whose image under this morphism has bounded height. This method provides a more general and simpler proof for a result of the first-named author and Najman on counting elliptic curves with prescribed level structures over number fields. We further include some examples of applications to modular curves.Keywords
All Related Versions
This publication has 6 references indexed in Scilit:
- Heights on stacks and a generalized Batyrev–Manin–Malle conjectureForum of Mathematics, Sigma, 2023
- Counting elliptic curves with prescribed level structures over number fieldsJournal of the London Mathematical Society, 2022
- Counting elliptic curves with an isogeny of degree threeProceedings of the American Mathematical Society, Series B, 2020
- Failures of weak approximation in familiesCompositio Mathematica, 2016
- Counting elliptic curves with prescribed torsionJournal für die reine und angewandte Mathematik (Crelles Journal), 2015
- Counting Lattice Points and O-Minimal StructuresInternational Mathematics Research Notices, 2013