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math.NT2025
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 \[…
math.NT2025
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…
math.NT2025
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…