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A uniform formula on the number of integer matrices with given determinant and height

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arxiv 2407.08191 v5 pith:7I3M3Z4Z submitted 2024-07-11 math.NT

Muhammad Afifurrahman This is my paper · ORCID
classification math.NT
keywords deltadeterminantformulaintegermatricesnumberabsoluteasymptotic
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abstract

We obtain an asymptotic formula for the number of integer $2\times 2$ matrices that have determinant $\Delta$ and whose absolute values of the entries are at most $H$. The result holds uniformly for a large range of $\Delta$ with respect to $H$.

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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. On commuting integer matrices

    math.NT 2025-04 accept novelty 7.0 of 10

    Commuting pairs of bounded 3x3 integer matrices are shown to number Theta(N^10), and 2x2 commuting pairs have an explicit asymptotic with constant 10 zeta(2)/(3 zeta(3)).

  2. Counting matrices over finite rank multiplicative groups

    math.NT 2025-02 accept novelty 6.0 of 10

    The paper proves upper bounds on the number of matrices with entries from a finite subset of a finite-rank multiplicative group that have a given rank, determinant, or characteristic polynomial.

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