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ON THE TRANSCENDENCE OF INFINITE SUMS OF VALUES OF RATIONAL FUNCTIONS

Published online by Cambridge University Press:  20 May 2003

N. SARADHA
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, [email protected]
R. TIJDEMAN
Affiliation:
Mathematical Institute, Leiden University, PO Box 9512, 2300 RA Leiden, [email protected]
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Abstract

Convergent sums $T = {\sum}_{n=1}^{\infty} P(n)/Q(n)$ and $U = {\sum}_{n=1}^{\infty}(-1)^n P(n)/Q(n)$, where $P(X), Q(X) \in {\mathbb Q}[X]$, and $Q(X)$ has only simple rational roots, are investigated. Adhikari, Shorey and the authors have shown that $T$ and $U$ are either rational or transcendental. Simple necessary and sufficient conditions are formulated for the transcendence of $T$ and $U$ if the degree of $Q$ is 3 and 2, respectively.

Keywords

Type
Research Article
Copyright
The London Mathematical Society 2003

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