33 citations · 87 across the 30 of their papers we have counts for
27 papers · 1 filter
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…
On Artin's conjecture on average and short character sums
Oleksiy Klurman, Igor E. Shparlinski, Joni Teräväinen
Let denote the number of primes up to for which the integer is a primitive root. We show that satisfies the asymptotic predicted by Artin's conjecture for…
Zeros of -functions and large partial sums of Dirichlet coefficients
Bryce Kerr, Oleksiy Klurman, Jesse Thorner
Let be an -function that satisfies a weak form of the generalized Ramanujan conjecture. We prove that large partial sums of str…
Sign changes of short character sums and real zeros of Fekete polynomials
Oleksiy Klurman, Youness Lamzouri, Marc Munsch
We discuss a general approach producing quantitative bounds on the number of sign changes of the weighted sums where is a fami…
norms and Mahler measure of Fekete polynomials
Oleksiy Klurman, Youness Lamzouri, Marc Munsch
We show that the distribution of the values of Fekete polynomials on the unit circle is governed, as , by an explicit limiting (non-Gaussian) random point process…
On Elliott's conjecture and applications
Oleksiy Klurman, Alexander P. Mangerel, Joni Teräväinen
Let be a multiplicative function. Under the merely necessary assumption that is non-pretentious (in the sense of Granville and Soundararajan), we s…
How negative can be?
Bryce Kerr, Oleksiy Klurman
Turán observed that logarithmic partial sums of completely multiplicative functions (in the particular case of the Liouville function ) ten…
On the random Chowla conjecture
Oleksiy Klurman, Ilya D. Shkredov, Max Wenqiang Xu
We show that for a Steinhaus random multiplicative function and any polynomial of which is not of the form $…
Beyond the Erdős discrepancy problem in function fields
Oleksiy Klurman, Alexander P. Mangerel, Joni Teräväinen
We characterize the limiting behavior of partial sums of multiplicative functions . In contrast to the number field setting, the characterization depends…
Monotone chains of Fourier coefficients of Hecke cusp forms
Oleksiy Klurman, Alexander Mangerel
We prove general equidistribution statements (both conditional and unconditional) relating to the Fourier coefficients of arithmetically normalized holomorphic Hecke cusp forms $f_…
Correlations of multiplicative functions in function fields
Oleksiy Klurman, Alexander P. Mangerel, Joni Teräväinen
We develop an approach to study character sums, weighted by a multiplicative function , of the form \begin{equation} \sum_{G\in \mathcal{M}_N}f(G)χ(G)ξ(G)…
On Positivity and Minimality for Second-Order Holonomic Sequences
George Kenison, Oleksiy Klurman, Engel Lefaucheux +5
An infinite sequence of real numbers is holonomic (also known as P-recursive or P-finite) if it satisfies a linear recurrence relation with p…
Multiplicative functions that are close to their mean
Oleksiy Klurman, Alexander P. Mangerel, Cosmin Pohoata +1
We introduce a simple sieve-theoretic approach to studying partial sums of multiplicative functions which are close to their mean value. This enables us to obtain various new resul…
Multiplicative functions in short arithmetic progressions
Oleksiy Klurman, Alexander P. Mangerel, Joni Teräväinen
We study for bounded multiplicative functions sums of the form \begin{align*} \sum_{\substack{n\leq x \atop n\equiv a\pmod q}}f(n), \end{align*} establishing that their varianc…
A note on multiplicative automatic sequences, II
Oleksiy Klurman, Pär Kurlberg
We prove that any -automatic multiplicative function either essentially coincides with a Dirichlet character, or vanishes on all sufficiently large p…
A note on multiplicative automatic sequences
Oleksiy Klurman, Pär Kurlberg
We prove that any -automatic completely multiplicative function essentially coincides with a Dirichlet character. This answers a question of J. P. Al…
On the Orbits of Multiplicative Pairs
Oleksiy Klurman, Alexander P. Mangerel
We characterize all pairs of completely multiplicative functions such that the orbit closure \[\overline{\{(f(n),g(n+1))\}_{n\ge 1}} \neq \mathbb{T}\t…
Polynomial products modulo primes and applications
Oleksiy Klurman, Marc Munsch
For any polynomial we study arithmetic dynamical systems generated by We apply this to…
Effective Asymptotic Formulae for Multilinear Averages of Multiplicative Functions
Oleksiy Klurman, Alexander P. Mangerel
Let be multiplicative functions taking values in the closed unit disc. Using an analytic approach in the spirit of Halász' mean…