English

An elementary proof of the irrationality of Tschakaloff series

Number Theory 2009-02-24 v1 Classical Analysis and ODEs

Abstract

We present a new proof of the irrationality of values of the series Tq(z)=n=0znqn(n1)/2T_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 Tq(z)T_q(z).

Keywords

Cite

@article{arxiv.math/0506086,
  title  = {An elementary proof of the irrationality of Tschakaloff series},
  author = {Wadim Zudilin},
  journal= {arXiv preprint arXiv:math/0506086},
  year   = {2009}
}

Comments

5 pages, AMSTeX