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

Published 11 Jul 2024 in math.NT | (2407.08191v5)

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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