## Irrationality of Fast Converging Series of Rational Numbers

J. Math. Sci. Univ. Tokyo
Vol. 8 (2001), No. 2, Page 275--316.

Duverney, Daniel
Irrationality of Fast Converging Series of Rational Numbers
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Abstract:
We say that the series of general term $u_n\not= 0$ is fast converging if $\log\vv{u_n}\leq c 2^n$ for some $c<0$. We prove irrationality results and compute irrationality measures for some fast converging series of rational numbers, by using Mahler's transcendence method in the form introduced by Loxton and Van der Poorten. With very weak assumptions on sequence $u_n$, this method allows to obtain only irrationality results.

Keywords: Fast converging series; irrationality; irrationality measures; Mahler's transcendence method

Mathematics Subject Classification (1991): 11J72, 11J82
Mathematical Reviews Number: MR1837165