Transcendence of some power series for Liouville number arguments
type: Item
instance of: scholarly article
title: Transcendence of some power series for Liouville number arguments
zbMATH Open document ID: 1437.11100
author: Fatma Çalişkan
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2018-07-31T00:00:00Z
review text: Let \(\{ a_n\}_{n=1}^\infty\) and \(\{ b_n\}_{n=1}^\infty\) be sequences of rational integers such that \(a_n>1\) for all positive integers \(n\). Assume that \(\limsup_{n\to\infty}\frac{\log\mid b_n\mid}{\log a_n} <1< \liminf_{n\to\infty}\frac{\log a_{n+1}}{\log a_n}\). Let \(\alpha\) be a Liouville number. Under the special conditions the author proves that the sum of the series \(\sum_{n=1}^\infty\frac{b_n}{a_n}\alpha^n\) eighter rational number or transcendental number. The author obtains similar results when \(b_n\) belong to finite algebraic number field and for \(p\)-adic cases.
reviewed by: Jaroslav Hančl
Mathematics Subject Classification ID: 11J81
Mathematics Subject Classification ID: 11J17
Mathematics Subject Classification ID: 11J61
zbMATH DE Number: 6911915
zbMATH Keywords: Liouville number
zbMATH Keywords: algebraic number field
zbMATH Keywords: \(p\)-adic number
zbMATH Keywords: power series
MaRDI profile type: Publication
full work available at URL: s12044-018-0407-2
OpenAlex ID: W2808426199
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Wikidata QID: Q129693995
DOI: 10.1007/S12044-018-0407-2
description: scientific article; zbMATH DE number 6911915