𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The structure of the spectra of Pisot numbers

✍ Scribed by Kevin G. Hare

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
252 KB
Volume
105
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

✦ Synopsis

For qAð1; 2Þ; Erdo¨s, Joo´and Komornik studied the set:

One item of interest that they examined is gap sizes of the form y kΓΎ1 Γ€ y k : In particular, they were interested in l m Γ°qÞ :ΒΌ lim infΓ°y kΓΎ1 Γ€ y k Þ and L m Γ°qÞ :ΒΌ lim supΓ°y kΓΎ1 Γ€ y k Þ:

This paper studies the distribution of the gap sizes y kΓΎ1 Γ€ y k of sets Y m Γ°qÞ: The techniques of Feng and Wen are extended to study the frequency of various gap sizes. Some computations are made for various q: A precise description of the gap frequencies in Y m Γ°qÞ is given when q is the golden ratio.

πŸ“œ SIMILAR VOLUMES

An Approximation Property of Pisot Numbe
An Approximation Property of Pisot Numbers
✍ Vilmos Komornik; Paola Loreti; Marco Pedicini πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 172 KB

Let q>1. Initiated by P. Erdo s et al. in [4], several authors studied the numbers l m (q)=inf [ y: y # 4 m , y{0], m=1, 2, ..., where 4 m denotes the set of all finite sums of the form y== 0 += 1 q+= 2 q 2 + } } } += n q n with integer coefficients &m = i m. It is known ([1], [4], [6]) that q is a

A classification of (some) Pisot-Cycloto
A classification of (some) Pisot-Cyclotomic numbers
✍ J.P. Bell; K.G. Hare πŸ“‚ Article πŸ“… 2005 πŸ› Elsevier Science 🌐 English βš– 166 KB

A complete classification of degree 2, 3 and degree 4 Pisot-Cyclotomic numbers is given. Some examples of higher degrees are also given. Pisot-Cyclotomic numbers have applications to quasicrystals and quasilattices.