An elementary proof of the irrationality of Tschakaloff series

Abstract

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

arXiv comment5 pages, AMSTeX

Cited by in corpus (1)

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