Dragan Stankov

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20182025

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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 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…