manuscripta mathematica

, Volume 107, Issue 4, pp 463–477 | Cite as

Remarks on irrationality of q-harmonic series

  • Wadim Zudilin


 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.


Positive Integer Linear Form Zeta Function Riemann Zeta Function Irrationality Measure 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Wadim Zudilin
    • 1
  1. 1.Moscow Lomonosov State University, Department of Mechanics and Mathematics, Vorobiovy Gory, GSP-2, 119992 Moscow, Russia. e-mail: wadim@ips.ras.ruRU

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