Topological torsion related to some recursive sequences of integers

✍ Scribed by Giuseppina Barbieri; Dikran Dikranjan; Chiara Milan; Hans Weber

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 313 KB
• Volume: 281
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200510650

✦ Synopsis

Abstract

For a recursively defined sequence u : = (u~n~) of integers, we describe the subgroup t~u~ (𝕋) of the elements x of the circle group 𝕋 satisfying lim~n~ u~n~x = 0. More attention is dedicated to the sequences satisfying a secondorder recurrence relation. In this case, we show that the size and the free‐rank of t~u~ (𝕋) is determined by the asymptotic behaviour of the ratios q~n~ = (u~n~ /u~n –1~) and we extend previous results of G. Larcher, C. Kraaikamp, and P. Liardet obtained from continued fraction expansion. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)