Remarks on irrationality of q-harmonic series

@article{Zudilin2002RemarksOI,
  title={Remarks on irrationality of q-harmonic series},
  author={W. Zudilin},
  journal={manuscripta mathematica},
  year={2002},
  volume={107},
  pages={463-477}
}
  • W. Zudilin
  • Published 2002
  • Mathematics
  • manuscripta mathematica
Abstract. We sharpen the known irrationality measures for the quantities , where z ? {±1} and p ?ℤ \ {0, ±1}. Our construction of auxiliary linear forms gives a q-analogue of the approach recently applied to irrationality problems for the values of the Riemann zeta function at positive integers. We also present a method for improving estimates of the irrationality measures of q-series. 
On the irrationality measure for a $ q$-analogue of $ \zeta(2)$
New irrationality measures for q-logarithms
Irrationality proof of certain Lambert series using little q-Jacobi polynomials
Diophantine Problems for q-Zeta Values
Arithmetic hypergeometric series
Multiple $q$-Zeta Values
N T ] 4 N ov 2 00 3 SÉRIES HYPERGÉOMÉTRIQUES BASIQUES , q-ANALOGUES DES
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ON APPROXIMATION MEASURES OF q-LOGARITHMS
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