Alina Ostafe

collaborators

9 papers

math.NT2026

Counting integer matrices with square-free determinants

Alina Ostafe, Igor E. Shparlinski

We consider the set $M_{n} (Z; H)$ of $n \times n$ -matrices with integer elements of size at most $H$ and obtain and asymptotic formula on the number of mat…

math.NT2026

On the sparsity of non-diagonalisable integer matrices and matrices with a given discriminant

Alina Ostafe, Igor E. Shparlinski

We consider the set $M_{n} (Z; H)$ of $n \times n$ -matrices with integer elements of size at most $H$ and obtain upper bounds on the number of matrices from $\mathcal…

math.NT2026

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.NT2026

Counting Irreducible polynomials with coefficients from thin subgroups

Alina Ostafe, Igor E. Shparlinski

L. Bary-Soroker and R. Shmueli (2026) have given an asymptotic formula for the number of irreducible polynomials over the finite fields $F_{q}$ of $q$ elements, such that the…

math.NT2025

Multiplicative dependence in the denominators of points of elliptic curves

Let $E_{1}, \dots, E_{s}$ be $s$ , not necessary distinct, elliptic curves over $Q$ . We give upper bounds on the frequency of $s$ -tuples of points in $E_1(\mathbb{Q})\times \…

math.DS2025

On quantum ergodicity for higher dimensional cat maps

PÃ¤r Kurlberg, Alina Ostafe, Zeev Rudnick +1

We study eigenfunction localization for higher dimensional cat maps, a popular model of quantum chaos. These maps are given by linear symplectic maps in ${\mathrm{Sp}}(2g,\mathbb Z…