Bartlomiej Bzdega

activity

20082016

most citedBounds on ternary cyclotomic coefficients

11 citations · 13 across the 3 of their papers we have counts for

collaborators

9 papers

math.NT2016

Cyclotomic polynomials at roots of unity

Bartlomiej Bzdega, Andres Herrera-Poyatos, Pieter Moree

The $n^{t h}$ cyclotomic polynomial $Φ_{n} (x)$ is the minimal polynomial of an $n^{t h}$ primitive root of unity. Hence $Φ_{n} (x)$ is trivially zero at primitive $n^{t h}$ roots of unity.…

math.NT2016

Products of cyclotomic polynomials on unit circle

Bartlomiej Bzdega

We present a method to deal with the values of polynomials of type $P (z) = \prod_{d \in D} (1 - z^{d})^{j_{d}}$ on the unit circle. We use it to improve the known bounds on various measures…

math.NT2014

On a generalization of Beiter Conjecture

Bartlomiej Bzdega

We prove that for every $ε > 0$ and a nonnegative integer $ω$ there exist primes $p_{1}, p_{2}, \dots, p_{ω}$ such that for $n = p_{1} p_{2} \dots p_{ω}$ the height of the cyclotomic polyno…

math.NT2013

On a certain family of inverse ternary cyclotomic polynomials

Bartlomiej Bzdega

We study a family of inverse ternary cyclotomic polynomials $Ψ_{pq r}$ in which $r \leq φ (pq)$ is a positive linear combination of $p$ and $q$ . We derive a formula for the height of su…

math.NT2013

Jumps of ternary cyclotomic coefficients

Bartlomiej Bzdega

It is known that two consecutive coefficients of a ternary cyclotomic polynomial $Φ_{pq r} (x) = \sum_{k} a_{pq r} (k) x^{k}$ differ by at most one. In this paper we give a criterion on $k$ t…

math.NT2012

Inclusion-exclusion polynomials with large coefficients

Bartlomiej Bzdega

We prove that for every positive integer $k$ there exist an inclusion-exclusion polynomial $Q_{{q_{1}, q_{2}, ..., q_{k}}}$ with the height at least $c^{2^k}\prod_{j=1}^{k-2}q_j^{2^{k-j-1…