Rational Points on Weighted projective Spaces

TL;DR

This paper develops an asymptotic formula for counting rational points on weighted projective spaces over number fields, extending Schanuel's results, and also considers the product spaces.

Contribution

It introduces a generalized asymptotic counting formula for rational points on weighted projective spaces and their products over number fields.

Findings

Derived an asymptotic formula generalizing Schanuel's heights

Counted rational points on product of weighted projective spaces

Extended counting methods to new geometric settings

Abstract

In this paper,we count the rational points on the weighted projective spaces defined over number fields w.r.t. ``size''. An asymptotic formula which generalizes the result of Schanuel's ``Heights in number fields'' is obtained. Furthermore, we count also the rational points on the product of weighted projective spaces.