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Journal of the London Mathematical Society Advance Access originally published online on July 31, 2009
Journal of the London Mathematical Society 2009 80(2):431-445; doi:10.1112/jlms/jdp029
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© 2009 London Mathematical Society

On the transcendence of some infinite sums

Pingzhi Yuan

School of Mathematics
South China Normal University
Guangzhou 510631
P.R. China
mcsypz@mail.sysu.edu.cn

Juan Li

Department of Mathematics
Sun Yat-sen University
Guangzhou 510275
P.R. China

In this paper we investigate the infinite convergent sum Formula , where Formula and Q(x) isin Q[x], and Q(x) has only simple rational zeros. N. Saradha and R. Tijdeman have obtained sufficient and necessary conditions for the transcendence of T if the degree of Q(x) is 3. In this paper we give sufficient and necessary conditions for the transcendence of T if the degree of Q(x) is 4 and Q(x) is reduced.

2000 Mathematics Subject Classification 11J81 (primary), 11J86, 11J91 (secondary).

The first author was supported by the Guangdong Provincial Natural Science Foundation (No. 8151027501000114) and NSF of China (No. 10571180).

Received August 6, 2007; revised February 6, 2009; published online July 31, 2009.


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