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Counting points on some genus zero Shimura curves

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arxiv 2504.09400 v2 pith:R7CC4XXA submitted 2025-04-13 math.NT

Tyler Genao , Tristan Phillips , Fredderick Saia , Tim Santens , John Yin This is my paper · ORCID
classification math.NT
keywords countingcurvesgenuspointsshimurasomezeroabelian
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abstract

We count certain abelian surfaces with potential quaternionic multiplication defined over a number field $K$ by counting points of bounded height on some genus zero Shimura curves.

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Cited by 1 Pith paper

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  1. Counting odd genus $2$ curves with a marked rational $3$-torsion point

    math.NT 2026-07 accept novelty 7.0 of 10

    The number of minimal monic odd-degree genus-2 Weierstrass models of height ≤ X with a marked rational Jacobian 3-torsion point is c X^10 + o(X^10) for an effectively computable constant c.

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