33 citations · 87 across the 30 of their papers we have counts for
34 papers
On the generation of multiplicative groups by small primes
Oleksiy Klurman, Igor E. Shparlinski, Joni Teräväinen
Motivated by a question of Regev arising from his improved quantum factoring algorithm, we study how many small primes are needed to generate the group $({\mathbb Z}/q{\mathbb Z})^…
Small values of signed harmonic sums and logarithmic means of multiplicative functions
Oleksiy Klurman, Marc Munsch, Yu-Chen Sun
We construct sequences with small values of signed harmonic sums \[ \sum_{n\in\mathcal{A}\cap[1,N]}\frac{a_n}{n}, \] for any reas…
A Halász-type asymptotic formula for logarithmic means and its consequences
Oleksiy Klurman, Alexander P. Mangerel
We establish an asymptotic formula for the logarithmic mean value of a 1-bounded multiplicative function that is sharp in many cases of interest. We derive from it a variety of app…
Irreducibility of polynomials with random multiplicative coefficients revisited
Oleksiy Klurman, Vlad Matei
We show that for a random polynomial \[ F(X) = \sum_{n=1}^{N} f(n) X^{n-1}, \] where is a random completely multiplicative function taking values in , one has \[…
Distribution of mixed character sums and extremal problems for Littlewood polynomials
Jonathan W. Bober, Oleksiy Klurman, Besfort Shala
We prove distributional results for mixed character sums \begin{equation*} \sum_{n\le x }χ(n)e(nθ), \end{equation*} for fixed and random character , as well…
On some classification problems of multiplicative functions
S. Kasjan, O. Klurman, M. Lemańczyk
We prove that a multiplicative function is Toeplitz if and only if there are a Dirichlet character and a finite subset of prime numbers such tha…