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Counting rational points on weighted projective spaces over number fields
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Counting rational points on weighted projective spaces over number fields
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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.
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Cited by 1 Pith paper
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Arithmetic Sparsity and Obstructions in Weighted Projective Spaces
The claimed asymptotic for weighted projective spaces, with a gcd(q, φ(me))^(-1) sparsity factor, is not established because the reduction to projective point counts ignores the Veronese map's non-surjectivity.
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