Topological torsion related to some recursive sequences of integers | Zendy

Barbieri Giuseppina | Zendy; Dikranjan Dikran | Zendy; Milan Chiara | Zendy; Weber Hans | Zendy

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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)

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