Transcendence of the values of certain series with Hadamard's gaps |
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| Authors: | T-A Tanaka |
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| Institution: | (1) Institute of Mathematics, Wrocław University, Plac Grunwaldzki 2-4, 50-384 Wrocław, Poland;; |
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| Abstract: | Transcendence of the number ?k=0￥ ark \sum_{k=0}^\infty \alpha^{r_k} , where a \alpha is an algebraic number with 0 < | a | \mid\alpha\mid > 1 and {rk}k\geqq0 \{r_k\}_{k\geqq0} is a sequence of positive integers such that limk?￥ rk+1/rk = d ? \mathbbN \{1} \lim_{k\to\infty}\, r_{k+1}/r_k = d \in \mathbb{N}\, \backslash \{1\} , is proved by Mahler's method. This result implies the transcendence of the number ?k=0￥ akdk \sum_{k=0}^\infty \alpha^{kd^k} . |
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