Muhammad Afifurrahman

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math.NT2024

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

Muhammad Afifurrahman

We obtain an asymptotic formula for the number of integer $2 \times 2$ matrices that have determinant $Δ$ and whose absolute values of the entries are at most $H$ . The result holds…

math.NT2024

Statistics of ranks, determinants and characteristic polynomials of rational matrices

Muhammad Afifurrahman, Vivian Kuperberg, Alina Ostafe +1

We consider the set of $n \times n$ matrices with rational entries having numerator and denominator of size at most $H$ and obtain upper and lower bounds on the number of such matri…

math.NT2023

Some counting questions for matrix products

Muhammad Afifurrahman

Given a set $X$ of $n \times n$ matrices and a positive integer $m$ , we consider the problem of estimating the cardinalities of the product sets $A_{1} \dots A_{m}$ , where $A_{i} \in X$ .…