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The Bombieri-Pila determinant method

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arxiv 2312.12890 v3 pith:XK4GZQ7W submitted 2023-12-20 math.NT math.AGmath.CO

Thomas F. Bloom , Jared Duker Lichtman This is my paper · ORCID
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keywords determinantmethodaccessiblealgebraicbombieribombieri-pilaclassicconcise
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We give a concise and accessible introduction to the real-analytic determinant method for counting integral points on algebraic curves, based on the classic 1989 paper of Bombieri and Pila.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Geometric Littlewood-Offord problems via lattice point counting

    math.CO 2025-05 accept novelty 8.0 of 10

    Geometric Littlewood-Offord probabilities are bounded by counting lattice points, resolving conjectures for varieties, convex-position sets, and bounded Chow-rank polynomials.

  2. The $abc$ conjecture is true almost always

    math.NT 2025-05 conditional novelty 2.0 of 10

    The number of exceptional coprime triples (a,b,c) with a+b=c≤N and rad(abc)<c^{1−ε} is at most O(N^{2/3}).

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