Journal of Mathematical Sciences

, Volume 146, Issue 2, pp 5669–5673 | Cite as

An elementary proof of the irrationality of Tschakaloff series

  • W. Zudilin


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


Rational Approximation Elementary Proof Golden Section Theta Series Analytic Number Theory 
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© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Department of Mechanics and MathematicsMoscow Lomonosov State UniversityMoscowRussia

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