Zur Transzendenz gewisser Reihen. (On the transcendence of certain series)
type: Item
instance of: scholarly article
title: Zur Transzendenz gewisser Reihen. (On the transcendence of certain series)
zbMATH Open document ID: 0601.10025
DOI: 10.1007/BF01547953
published in: Monatshefte für Mathematik
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178351
review text: W. M. Schmidt's famous theorem on the simultaneous approximation of algebraic numbers is used to derive transcendence results concerning certain series of rational numbers. The denominators of these numbers are taken from finitely many linear recursive sequences with the same characteristic polynomial which in turn is the minimal polynomial of a PV number. These denominators have to satisfy a divisibility as well as a growth condition (and in an appendix of the paper the second author studies the connections between these two kinds of hypotheses). The nominators of the rational terms of the series must satisfy some growth conditions too. One section of the present paper is devoted to the study of the implications of Mahler's analytic transcendence method from 1929 to the arithmetical questions considered here.
Mathematics Subject Classification ID: 11J81
Mathematics Subject Classification ID: 11R06
Mathematics Subject Classification ID: 11B37
zbMATH DE Number: 3968683
zbMATH Keywords: simultaneous approximation of algebraic numbers
zbMATH Keywords: transcendence
zbMATH Keywords: series of rational numbers
zbMATH Keywords: linear recursive sequences
zbMATH Keywords: PV number
author: Peter Bundschuh
author: Attila Pethő
MaRDI profile type: Publication
cites work: Q3916657
cites work: A note on recurring series
cites work: Q5541455
cites work: Q4123397
cites work: Perfect powers in second order linear recurrences
cites work: Q4112054
cites work: On two theorems of Gelfond and some of their applications
cites work: Über simultane Approximation algebraischer Zahlen durch rationale
cites work: Simultaneous approximation to algebraic numbers by rationals
OpenAlex ID: W154642331
description: scientific article; zbMATH DE number 3968683