On number system constructions

被引：0
|
作者：
L. Germán
A. Kovács
机构：
[1] Eötvös Loránd University,Department of Computer Algebra
来源：
Acta Mathematica Hungarica | 2007年 / 115卷
关键词：
number system; radix representation; 11A63;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We investigate various number system constructions. After summarizing earlier results we prove that for a given lattice Λ and expansive matrix M: Λ → Λ if ρ(M−1) < 1/2 then there always exists a suitable digit set D for which (Λ, M, D) is a number system. Here ρ means the spectral radius of M−1. We shall prove further that if the polynomial f(x) = c0 + c1x + ··· + ckxk ∈ Z[x], ck = 1 satisfies the condition |c0| > 2 Σi=1k |ci| then there is a suitable digit set D for which (Zk, M, D) is a number system, where M is the companion matrix of f(x).
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页码：155 / 167
页数：12
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