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Journal of Mathematical Sciences

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

An elementary proof of the irrationality of Tschakaloff series

  • W. Zudilin
Article
  • 31 Downloads

Abstract

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).

Keywords

Rational Approximation Elementary Proof Golden Section Theta Series Analytic Number Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

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

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