This book is designed for a topics course in computational number theory. It is based around
a number of difficult old problems that live at the interface of analysis and number theory …

It was discovered some years ago that there exist non-integer real numbers q> 1 for which
only one sequence (ci) of integers ci∈[0, q) satisfies the equality∑ i= 1∞ ciq− i= 1. The set …

Internationally recognised researchers look at developing trends in combinatorics with
applications in the study of words and in symbolic dynamics. They explain the important …

By the m-spectrum of a real number q> 1 we mean the set Ym (q) of values p (q) where p
runs over the height m polynomials with integer coefficients. These sets have been …

In this paper, we prove that, for β∈ ℂ, every α∈ ℂ has at most finitely many (possibly none
at all) representations of the form α= dn⁢ β n+ dn-1⁢ β n-1+…+ d 0 with nonnegative …

This paper is based on a talk given at WWCA (Waterloo Workshop on Computer Algebra)
held at Wilfird Laurier University, April 2006. This paper gives a history of beta-expansions …

For a real number $\beta> 1$, Erdős, Joó and Komornik study distances between
consecutive points in the set\[X^ m (\beta)=\Bigl\{\sum _ {j= 0}^ n a_j\beta^ j: n\in\mathbb {N} …

For every positive integer $ n $, we introduce a set $\mathcal {T} _n $ made of $(n+ 3)^ 2$
Wang tiles (unit squares with labeled edges). We represent a tiling by translates of these …

The spectrum of a real number β> 1 is the set X m (β) of p (β) where p ranges over all
polynomials with coefficients restricted to A={0, 1,…, m}. For a quadratic Pisot unit β, we …

For q∈(1, 2), Erdös, Joó and Komornik studied the set:[Formula: see text] One item of
interest that they examined is gap sizes of the form yk+ 1− yk. In particular, they were …