22 citations · 34 across the 17 of their papers we have counts for
15 papers · 1 filter
Counting integer polynomials with several roots of maximal modulus
Artūras Dubickas, Min Sha
In this paper, for positive integers and , we obtain some estimates on the cardinality of the set of monic integer polynomials of degree and height bounded by …
Euclidean minima of algebraic number fields
Artūras Dubickas, Min Sha, Igor E. Shparlinski
In this paper, we use some of our previous results to improve an upper bound of Bayer-Fluckiger, Borello and Jossen on the Euclidean minima of algebraic number fields. Our bound de…
Linear relations with conjugates of a Salem number
Artūras Dubickas, Jonas Jankauskas
In this paper we consider linear relations with conjugates of a Salem number . We show that every such a relation arises from a linear relation between conjugates of the corresp…
Counting decomposable polynomials with integer coefficients
Artūras Dubickas, Min Sha
A polynomial over a ring is called decomposable if it is a composition of two nonlinear polynomials. In this paper, we obtain sharp lower and upper bounds for the number of decompo…
The distance to square-free polynomials
Artūras Dubickas, Min Sha
In this paper, we consider a variant of Turán's problem on the distance from an integer polynomial in to the nea\-rest irreducible polynomial in . We…
On the number of integer polynomials with multiplicatively dependent roots
Arturas Dubickas, Min Sha
In this paper, we give some counting results on integer polynomials of fixed degree and bounded height whose distinct non-zero roots are multiplicatively dependent. These include s…