An elementary proof of the irrationality of Tschakaloff series

Details An elementary proof of the irrationality of Tschakaloff series An elementary proof of the irrationality of Tschakaloff series

2005-06-05

arxiv.org/abs/math/0506086v1

Fundam. Prikl. Mat. 11:6 (2005), 59--64; English transl., J. Math. Sci. 146 (2007), no. 2, 5669--5673

Mathematics

Number Theory

5 pages, AMSTeX

Scientific paper

10.1007/s10958-007-0382-0

We present a new proof of the irrationality of values of the series
$T_q(z)=\sum_{n=0}^\infty z^nq^{-n(n-1)/2}$ in both qualitative and
quantitative forms. The proof is based on a hypergeometric construction of
rational approximations to $T_q(z)$.

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