Author

Alina Ostafe

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Preprint Oct 2026

Systems of equations with elements of finitely generated groups and with linear recurrence sequences

We obtain new and essentially optimal bounds on the number of solutions of diagonal systems of $k$ polynomial equations in $s$ variables from an arbitrary finite subset of a finitely generated group in a field of characteristic zero. Our bounds generalise and sometimes improve previous results of J. Bourgain, M. Z. Gar...

Subham Bhakta, Alina Ostafe, Igor E. Shparlinski · 0 citations

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. · 0 citations