137 research outputs found
Additive unit representations in global fields - A survey
We give an overview on recent results concerning additive unit
representations. Furthermore the solutions of some open questions are included.
The central problem is whether and how certain rings are (additively) generated
by their units. This has been investigated for several types of rings related
to global fields, most importantly rings of algebraic integers. We also state
some open problems and conjectures which we consider to be important in this
field.Comment: 13 page
Linear recursive odometers and beta-expansions
The aim of this paper is to study the connection between different properties
related to -expansions. In particular, the relation between two
conditions, both ensuring pure discrete spectrum of the odometer, is analysed.
The first one is the so-called Hypothesis B for the -odometers and the
second one is denoted by (QM) and it has been introduced in the framework of
tilings associated to Pisot -numerations
On the discrepancy of some special sequences
AbstractWe obtain estimates for the discrepancy of the sequence (xs(d)(q;n))n=0∞, where s(d)(q;n) denotes the sum of the dth powers of the q-ary digits of the nonnegative integer n and x is an irrational number of finite approximation type. Furthermore metric results for a similar type of sequences are given
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