Universität zu Köln

Bundschuh, Peter and Vaananen, Keijo (2015). ALGEBRAIC INDEPENDENCE OF RECIPROCAL SUMS OF POWERS OF CERTAIN FIBONACCI-TYPE NUMBERS. Funct. Approx. Comment. Math., 53 (1). S. 47 - 69. POZNAN: WYDAWNICTWO NAUKOWE UAM. ISSN 0208-6573

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Abstract

The Fibonacci-type numbers in the title look like R-n = g(1)gamma(n)(1) + g(2)gamma(n)(2) and S-n = h(1)gamma(n)(1) + h(2)gamma(n)(2) for any n is an element of Z, where the g's, h's, and gamma's are given algebraic numbers satisfying certain natural conditions. For fixed k is an element of Z(>0), and for fixed non-zero periodic sequences (a(h)), (b(h)), (c(h)) of algebraic numbers, the algebraic independence of the series Sigma(infinity)(h=0) a(h)/gamma(krh)(1), Sigma(infinity)(h=0)' b(h)/(R-kr(+l)h)(m), Sigma(infinity)(h=0)' c(h)/(S-kr(+l)h)(m) ((l, m, r) is an element of z x z(>0) x z(>1)) is studied. Here the main tool is Mahler's method which reduces the investigation of the algebraic independence of numbers (over Q) to that of functions (over the rational function field) if they satisfy certain types of 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:38-395502
DOI:	10.7169/facm/2015.53.1.4
Journal or Publication Title:	Funct. Approx. Comment. Math.
Volume:	53
Number:	1
Page Range:	S. 47 - 69
Date:	2015
Publisher:	WYDAWNICTWO NAUKOWE UAM
Place of Publication:	POZNAN
ISSN:	0208-6573
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 Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/39550