Preprint
Aug 2026
The divisor function for matrices
We introduce a matrix divisor function $\tau_n(T,M)$, counting factorisations $AB=M$ for $n\times n$ integer matrices $A,B$ of height at most $T$. For a fixed non-singular $M$, or for the zero matrix $M=O_n$, we prove an asymptotic formula for $\tau_n(T,M)$, as $T\to \infty$, using lattice point counting. We also prove...
Tim Browning, N. Kalinin, Alina Ostafe et al.
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