Universität zu Köln

Bundschuh, Peter and Vaananen, Keijo (2018). Note on the Stern-Brocot sequence, some relatives, and their generating power series. J. Theor. Nr. Bordx., 30 (1). S. 195 - 203. TALENCE: UNIV BORDEAUX, INST MATHEMATIQUES BORDEAUX. ISSN 1246-7405

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Abstract

Three variations on the Stern-Brocot sequence are related to the celebrated Thue-Morse sequence. In the present note, the generating power series of these four sequences are considered. Whereas one of these was known to define a rational function, the other three are proved here to be algebraically independent over C(z). Then this statement is fairly generalized by including the functions Phi(z), Phi(-z), Psi(z), Psi(z(2)), where Phi and Psi denote the generating power series of the Rudin-Shapiro and Baum-Sweet sequence, respectively. Moreover, some arithmetical applications are given.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Bundschuh, Peter UNSPECIFIED UNSPECIFIED UNSPECIFIED Vaananen, Keijo UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-199904
Journal or Publication Title:	J. Theor. Nr. Bordx.
Volume:	30
Number:	1
Page Range:	S. 195 - 203
Date:	2018
Publisher:	UNIV BORDEAUX, INST MATHEMATIQUES BORDEAUX
Place of Publication:	TALENCE
ISSN:	1246-7405
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language ALGEBRAIC INDEPENDENCE; EQUATIONS Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/19990