L'aszl'o M'erai

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20232025

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math.NT2023

Number of characteristic polynomials of matrices with bounded height

László Mérai, 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 and lower bounds on the number of distinct irr…

math.NT2023

Smooth polynomials with several prescribed coefficients

László Mérai

Let $F_{q} [t]$ be the polynomial ring over the finite field $F_{q}$ of $q$ elements. A polynomial in $F_{q} [t]$ is called $m$ -smooth (or $m$ -friable) if all it…

math.NT2023

Distribution of recursive matrix pseudorandom number generator modulo prime powers

László Mérai, Igor E. Shparlinski

Given a matrix $A \in GL_{d} (Z)$ . We study the pseudorandomness of vectors $u_{n}$ generated by a linear recurrent relation of the form $$ \mathbf{u}_{n+1} \e…