ON NEWMAN POLYNOMIALS WHICH DIVIDE NO LITTLEWOOD POLYNOMIAL (2009)
Artūras Dubickas, Jonas Jankauskas
Abstract. Recall that a polynomial P(x) ∈ Z[x] with coefficients 0,1 and constant term 1 is called a Newman polynomial, whereas a polynomial with coefficients −1,1 is called a Littlewood...
Auxiliary polynomials for some problems regarding Mahler’s measure (2009)
Artūras Dubickas, J. Mossinghoff
Abstract. We describe an iterative method of constructing some favorable auxiliary polynomials used to obtain lower bounds in some problems of algebraic number theory. With this method we improve a...
MATHEMATICS OF COMPUTATION S 0025-5718(09)02211-X (2009)
Lower Bounds, For Z-numbers, Artūras Dubickas, J. Mossinghoff
Abstract. Let p/q be a rational noninteger number with p>q ≥ 2. A real number λ>0isaZ p/q-number if {λ(p/q) n} < 1/q for every nonnegative integer n, where{x} denotes the fractional part...
LOWER BOUNDS FOR Z-NUMBERS (2008)
Artūras Dubickas, J. Mossinghoff
Abstract. Let p/q be a rational noninteger number with p> q ≥ 2. A real number λ> 0 is a Z p/q-number if {λ(p/q) n} < 1/q for every nonnegative integer n, where {x} denotes the...
Partitions of positive integers into sets without infinite progressions (2008)
We prove a result which implies that, for any real numbers $a$ and $b$ satisfying $0 leq a leq b leq 1$, there exists an infinite sequence of positive integers $A$ with lower density $a$ and upper...
Refinement Equations and Spline Functions (2008)
Dubickas, Artūras, Xu, Zhiqiang
In this paper, we exploit the relation between the regularity of refinable functions with non-integer dilations and the distribution of powers of a fixed number modulo 1, and show the nonexistence of...
Infinite Sets of Integers Whose Distinct Elements Do Not Sum to a Power (2008)
Artūras Dubickas, Paulius ˇ Sarka
We first prove two results which both imply that for any sequence B of asymptotic density zero there exists an infinite sequence A such that the sum of any number of distinct elements of A does not...