Artūras Dubickas

Arithmetical Properties of Powers of Algebraic Numbers

We consider the sequences of fractional parts

Refinement equations and spline functions

\{\xi \alpha^n\}, n \,{=}\,1,2,3,\dots,

Counting and Testing Dominant Polynomials

and of integer parts

An approximation by lacunary sequence of vectors

[\xi \alpha^n], n \,{=}\,1,2,3,\dots,

ON SUBFIELDS OF A FIELD GENERATED BY TWO CONJUGATE ALGEBRAIC NUMBERS

where

On the supremum of the representation function of a sumset

\xi

On Newman polynomials which divide no Littlewood polynomial

is an arbitrary positive number and

On numbers which are differences of two conjugates of an algebraic integer

\alpha\,{>}\,1

ON THE FRACTIONAL PARTS OF RATIONAL POWERS

is an algebraic number. We obtain an inequality for the difference between the largest and the smallest limit points of the first sequence. Such an inequality was earlier known for rational

ZEROS OF THE ESTERMANN ZETA FUNCTION

\alpha