THE MINIMAL GROWTH OF A k-REGULAR SEQUENCE

被引：15

作者：

Bell, Jason P. ^{[1
]}

Coons, Michael ^{[2
]}

Hare, Kevin G. ^{[1
]}

机构：

[1] Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada

[2] Univ Newcastle, Sch Math & Phys Sci, Callaghan, NSW 2308, Australia

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2014年 / 90卷 / 02期

基金：

加拿大自然科学与工程研究理事会; 澳大利亚研究理事会;

关键词：

automata sequences; regular sequences; growth of arithmetic functions;

D O I：

10.1017/S0004972714000197

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We determine a lower gap property for the growth of an unbounded Z-valued k-regular sequence. In particular, if f : N -> Z is an unbounded k-regular sequence, we show that there is a constant c > 0 such that vertical bar f (n)vertical bar > c log n infinitely often. We end our paper by answering a question of Borwein, Choi and Coons on the sums of completely multiplicative automatic functions.

引用

页码：195 / 203

页数：9

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