Alexandros Kalogirou

activity

20242026

collaborators

4 papers

math.NT2026

Small sums of roots of unity

Alexandros Kalogirou

We address the question of how small a non-vanishing sum of $N$ -th roots of unity with $k$ terms can be. We show upper bounds of the shape $N^{- I^\pm_{k}}$ , where $Î±_k\rightarrow\infty…

math.NT2025

On the irreducibility of the non-cyclotomic part of most 0,1-polynomials with few terms

Michael Filaseta, Alexandros Kalogirou

We provide an alternative exposition of a result due to Schinzel. Fix an integer $k \geq 2$ . For almost all choices of positive integers $n_{1} < \dots < n_{k}$ , we show that the p…

math.NT2024

Irreducibility of lacunary polynomials with 0,1 coefficients

Alexandros Kalogirou

We show that $0, 1$ -polynomials of high degree and few terms are irreducible with high probability. Formally, let $k \in N$ and $F (x) = 1 + \sum_{i = 1}^{k} x^{n_{i}}$ , where $ 0<n_1<\c…

math.NT2024

Covering systems with the sum of the reciprocals of the moduli close to $1$

Michael Filaseta, Alexandros Kalogirou

In 1952, H. Davenport posed the problem of determining a condition on the minimum modulus $m_{0}$ in a finite distinct covering system that would imply that the sum of the reciproc…

Small sums of roots of unity

On the irreducibility of the non-cyclotomic part of most 0,1-polynomials with few terms

Irreducibility of lacunary polynomials with 0,1 coefficients

Covering systems with the sum of the reciprocals of the moduli close to 1

Covering systems with the sum of the reciprocals of the moduli close to $1$