Universität zu Köln

Bundschuh, Peter and Vaananen, Keijo (2015). Algebraic independence of the generating functions of the Stern polynomials and their twisted analogues. Arch. Math., 105 (2). S. 139 - 149. BASEL: SPRINGER BASEL AG. ISSN 1420-8938

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Abstract

Dilcher and Stolarsky introduced and studied a polynomial analogue of Stern's diatomic sequence. Similarly, we define here a polynomial analogue of Bacher's twisted version of the Stern sequence. Our main aim is to consider the two-dimensional generating functions of both these polynomial sequences. More precisely, since they satisfy certain Mahler-type functional equations, we succeed in characterizing the algebraic independence over of the values of these two functions at algebraic points with 0 broken vertical bar xi broken vertical bar, broken vertical bar alpha broken vertical bar < 1

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:38-397613
DOI:	10.1007/s00013-015-0789-7
Journal or Publication Title:	Arch. Math.
Volume:	105
Number:	2
Page Range:	S. 139 - 149
Date:	2015
Publisher:	SPRINGER BASEL AG
Place of Publication:	BASEL
ISSN:	1420-8938
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 SEQUENCE; TRANSCENDENCE Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/39761