Jonathan Chapman

collaborators

3 papers

math.NT2026

Counting $2 \times 2$ integer matrices with a given determinant

Jonathan Chapman, Akshat Mudgal

Given positive integers $h, N$ satisfying $1 ⩽ h ⩽ 2 N^{2}$ , we define $T (h, N)$ to be the number of $2 \times 2$ integer matrices with determinant equal to $h$ whose en…

math.NT2026

Counting solutions to the quadratic determinant equation

Jonathan Chapman, Akshat Mudgal

Given $h, N \in N$ satisfying $1 ⩽ h ⩽ N^{2}$ , we prove an asymptotic formula for the number of solutions to the equation $x_{1} x_{2} - x_{3} x_{4} = h$ with $x_1,…

math.NT2025

On commuting integer matrices

Jonathan Chapman, Akshat Mudgal

Given $d, N \in N$ , we define $C_{d} (N)$ to be the number of pairs of $d \times d$ matrices $A, B$ with entries in $[- N, N] \cap Z$ such that $A B = B A$ . We…

Counting 2×2 integer matrices with a given determinant

Counting solutions to the quadratic determinant equation

On commuting integer matrices

Counting $2 \times 2$ integer matrices with a given determinant