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Transcendence of a fast converging series of rational numbers

Published online by Cambridge University Press:  26 March 2001

DANIEL DUVERNEY
DANIEL DUVERNEY
Affiliation:
24 Place du Concert, F-59800 Lille, France. E-mail: dduverney@nordnet.fr
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Abstract

Let a ∈ ℕ [setmn ] {0, 1} and let bn be a sequence of rational integers satisfying bn = O(η−2n) for every η ∈]0, 1[. We prove that the number S = [sum ]+∞n=0 1/(a2n + bn) is transcendental by using a special form of Mahler's transcendence method.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 130 , Issue 2 , March 2001 , pp. 193 - 207
Copyright
2001 Cambridge Philosophical Society

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