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Topological torsion related to some recursive sequences of integers
Author(s) -
Barbieri Giuseppina,
Dikranjan Dikran,
Milan Chiara,
Weber Hans
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510650
Subject(s) - mathematics , combinatorics , rank (graph theory) , sequence (biology) , torsion (gastropod) , discrete mathematics , topology (electrical circuits) , medicine , genetics , surgery , biology
For a recursively defined sequence u : = ( u n ) of integers, we describe the subgroup t u () of the elements x of the circle group satisfying lim nu 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 () 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)