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Construction of some special subsequences within a Farey sequence

Basu-Mallick, B and Bhattacharyya, Tanaya and Sen, Diptiman (2003) Construction of some special subsequences within a Farey sequence. [Preprint]

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Abstract

Recently it has been found that some special subsequences within a Farey sequence play a crucial role in determining the ranges of coupling constant for which quantum soliton states can exist for an integrable derivative nonlinear Schrodinger model. In this article, we find a novel mapping which connects two such subsequences belonging to Farey sequences of different orders. By using this mapping, we construct an algorithm to generate all of these special subsequences within a Farey sequence. We also derive the continued fraction expansions for all the elements belonging to a subsequence and observe a close connection amongst the corresponding expansion coefficients.

Item Type: Preprint
Keywords: Number Theory
Department/Centre: Division of Physical & Mathematical Sciences > Centre for Theoretical Studies
Date Deposited: 31 Jul 2004
Last Modified: 19 Sep 2010 04:13
URI: http://eprints.iisc.ernet.in/id/eprint/755

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