Construction of some special subsequences within a Farey sequence
Basu-Mallick, B. ; Bhattacharyya, Tanaya ; Sen, Diptiman
arXiv, 0312021 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2003-12-09
Classification:  Mathematical Physics,  High Energy Physics - Theory,  Mathematics - Number Theory,  Nonlinear Sciences - Exactly Solvable and Integrable Systems 
@article{0312021,
     author = {Basu-Mallick, B. and Bhattacharyya, Tanaya and Sen, Diptiman},
     title = {Construction of some special subsequences within a Farey sequence},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0312021}
}

Basu-Mallick, B.; Bhattacharyya, Tanaya; Sen, Diptiman. Construction of some special subsequences within a Farey sequence. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0312021/