L'aszl'o M'erai

activity

20232025

collaborators

5 papers

math.NT2025

On the Dynamical System Generated by the Möbius Transformation at Smooth Times

László Mérai, Igor E. Shparlinski

We study the distribution of the sequence of the first $N$ elements of the discrete dynamical system generated by the Möbius transformation $x \mapsto (α x + β) / (γ x + δ)$ over a fin…

math.NT2024

Rudin-Shapiro function along irreducible polynomials over finite fields

László Mérai

Let $q$ be an odd prime power and $F_{q}$ be the finite field of $q$ elements. We define the Rudin-Shapiro function $R$ on monic polynomials $f=t^n+f_{n-1}t^{n-1}+\dots + f_…

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…