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.
144, Cambridge University Press, 2001
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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.