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The density of ADE families of curves having squarefree discriminant

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arxiv 2306.05961 v3 pith:AMF7BB7M submitted 2023-06-09 math.NT

Martí Oller This is my paper · ORCID
classification math.NT
keywords curvesdensitybhargavadiscriminantfamilieshavingrepresentationssquarefree
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We determine the density of curves having squarefree discriminant in some families of curves that arise from Vinberg representations, showing that the global density is the product of the local densities. We do so using the framework of Thorne and Laga's PhD theses and Bhargava's orbit-counting techniques. This paper generalises a previous result by Bhargava, Shankar and Wang. As an application, we give an asymptotic for the number of reducible orbits of our representations.

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  1. Squarefree discriminants of polynomials with prime coefficients

    math.NT 2025-01 reject novelty 6.0 of 10

    The paper derives asymptotic formulas for prime-coefficient polynomials with squarefree discriminant, with the non-monic maximal-order portion of Theorem 1.1 invalid as stated.

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