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Palindromic Sequences of the Markov Spectrum

Name: Palindromic Sequences of the Markov Spectrum
Creator: Matty van-Son
Keywords: Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT), 0102 computer and information sciences, 0101 mathematics, 01 natural sciences, 11B99

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Sep 2019Embargo end date: 01 Jan 2018Publisher:Pleiades Publishing LtdJournal:Mathematical Notes, volume 106, pages 457-467 (issn: 0001-4346, eissn: 1573-8876,

Authors: Matty van-Son;

doi: 10.1134/s0001434619090153 , 10.48550/arxiv.1804.10802

arXiv: http://arxiv.org/abs/1804.10802

Palindromic Sequences of the Markov Spectrum

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Abstract

We study the periods of Markov sequences, which are derived from the continued fraction expression of elements in the Markov spectrum. This spectrum is the set of minimal values of indefinite binary quadratic forms that are specially normalised. We show that the periods of these sequences are palindromic after a number of circular shifts, the number of shifts being given by Stern's diatomic sequence.

Related Organizations

University of Liverpool
United Kingdom

Keywords

Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT), 11B99

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