Corpus ID: 9784502

On the irrationality measure for a q-analogue of ζ(2)

  title={On the irrationality measure for a q-analogue of $\zeta$(2)},
  author={Wadim Zudilin},
A Liouville-type estimate is proved for the irrationality measure of the quantities ζq(2) = ∞ ∑ n=1 q (1− qn)2 with q−1 ∈ Z \ {0,±1}. The proof is based on the application of a q-analogue of the arithmetic method developed by Chudnovsky, Rukhadze, and Hata and of the transformation group for hypergeometric series — the group-structure approach introduced by Rhin and Viola. Bibliography: 21 titles. Introduction For a complex number q, |q| < 1, we consider the quantities 
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