Dragan Stankov

activity

20132025

most citedOn linear combinations of Chebyshev polynomials

5 citations · 11 across the 8 of their papers we have counts for

collaborators

10 papers

math.NT2025

Approximation of the number of nonunimodular zeros of a self-reciprocal polynomial

Dragan Stankov

We introduce the ratio of the number of roots, not equal to 1 in modulus, of a reciprocal polynomial $R_{d} (x)$ to its degree $d$ . For some sequences of reciprocal polynomials we sho…

math.NT2025

The alternative to Mahler measure of a multivariate polynomial

Dragan Stankov

We introduce the ratio of the number of roots of a polynomial $P_{d}$ , less than one in modulus, to its degree $d$ as an alternative to Mahler measure. We investigate some properti…

math.NT2022

The number of nonunimodular roots of a reciprocal polynomial

Dragan Stankov

We introduce a sequence P_d of monic reciprocal polynomials with integer coefficients having the central coefficients fixed as well as the peripheral coefficients. We prove that th…

math.NT2019

The number of unimodular roots of some reciprocal polynomials

Dragan Stankov

We introduce a sequence $P_{2 n}$ of monic reciprocal polynomials with integer coefficients having the central coefficients fixed. We prove that the ratio between number of nonunimo…

math.NT2018

The reciprocal algebraic integers having small houses

Dragan Stankov

Let $α$ be an algebraic integer of degree $d$ , which is reciprocal. The house of $α$ is the largest modulus of its conjugates. We proved that $d$ -th power of the house of reciproca…

math.NT2018

The House of a Reciprocal Algebraic Integer

Dragan Stankov

Let $α$ be an algebraic integer of degree $d$ , which is reciprocal. The house of $α$ is the largest modulus of its conjugates. We compute the minimum of the houses of all reciproca…

math.NT2017★ 4 cited

The necessary and sufficient condition for an algebraic integer to be a Salem number

Dragan Stankov

We present a necessary and sufficient condition for a root greater than unity of a monic reciprocal polynomial of an even degree at least four, with integer coefficients, to be a S…

math.NT2015★ 2 cited

On distribution modulo 1 of the sum of powers of a Salem number

Dragan Stankov

Let $θ$ be a Salem number and $P (x)$ a polynomial with integer coefficients. It is well-known that the sequence $(θ^{n})$ modulo 1 is dense but not uniformly distributed. In this art…

math.NT2014

Boyd's conjecture

Dragan Stankov

We determine the limit of the rate $\frac{ν _{n, a}}{n}$ between the number $ν_{n, a}$ of roots of the trinomial $x^{n} - a x - 1$ , $a \in (0, 2]$ , which are greater than 1 in modulus, and deg…

math.NT2013★ 5 cited

On linear combinations of Chebyshev polynomials

Dragan Stankov

We investigate an infinite sequence of polynomials of the form: \[a_0T_{n}(x)+a_{1}T_{n-1}(x)+\cdots+a_{m}T_{n-m}(x)\] where $(a_{0}, a_{1}, \dots, a_{m})$ is a fixed m-tuple of real numbe…