O. Gorodetsky

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math.NT2024

High and odd moments in the Erdős--Kac theorem

Ofir Gorodetsky

Granville and Soundararajan showed that the $k$ th moment in the Erdős--Kac theorem is equal to the $k$ th moment of the standard Gaussian distribution in the range $k=o((\log \log x…

math.NT2018

Irreducible polynomials over $F_{2^{r}}$ with three prescribed coefficients

Ofir Gorodetsky

For any positive integers $n \geq 3$ and $r \geq 1$ , we prove that the number of monic irreducible polynomials of degree $n$ over $F_{2^{r}}$ in which the coefficients of $T^{…

math.NT2018

q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon

Ofir Gorodetsky

We establish a supercongruence conjectured by Almkvist and Zudilin, by proving a corresponding $q$ -supercongruence. Similar $q$ -supercongruences are established for binomial coeffi…

math.NT2018

Roots of Polynomials and The Derangement Problem

Lior Bary-Soroker, Ofir Gorodetsky

We present a new killing-a-fly-with-a-sledgehammer proof of one of the oldest results in probability which says that the probability that a random permutation on $n$ elements has n…

High and odd moments in the Erdős--Kac theorem

Irreducible polynomials over F2r​ with three prescribed coefficients

q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon

Roots of Polynomials and The Derangement Problem

Irreducible polynomials over $F_{2^{r}}$ with three prescribed coefficients