Universität zu Köln

Bundschuh, Peter and Vaananen, Keijo (2016). Some Arithmetical Results on Reciprocal Sums of Certain Fibonacci-Type Numbers. Southeast Asian Bull. Math., 40 (6). S. 797 - 815. KUNMING: SOUTHEAST ASIAN MATHEMATICAL SOC-SEAMS. ISSN 0219-175X

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Abstract

First, closed form evaluations of series generalizing Sigma 1/F-2k, are resumed. Next, transcendence proofs of Sigma 1/F-dk for integers d > 2 by Roth's approximation theorem, or by Mahler's analytic method are recalled. This second method leads to far-reaching transcendence and algebraic independence results on series, where the Fibonaccis F-n are replaced by more general expressions. These questions, making up the greatest part of the work, include studies of the transcendence over C(z) of the solutions of certain functional equations.

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:38-288256
Journal or Publication Title:	Southeast Asian Bull. Math.
Volume:	40
Number:	6
Page Range:	S. 797 - 815
Date:	2016
Publisher:	SOUTHEAST ASIAN MATHEMATICAL SOC-SEAMS
Place of Publication:	KUNMING
ISSN:	0219-175X
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 SERIES Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/28825