New irrationality measures for $q$-logarithms
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- by Tapani Matala-aho, Keijo Väänänen and Wadim Zudilin PDF
- Math. Comp. 75 (2006), 879-889 Request permission
Abstract:
The three main methods used in diophantine analysis of $q$-series are combined to obtain new upper bounds for irrationality measures of the values of the $q$-logarithm function \[ \ln _{q}(1-z)=\sum _{\nu =1}^{\infty }\frac {z^{\nu }q^{\nu }}{1-q^{\nu }}, \qquad |z|\leqslant 1,\] when $p=1/q\in \mathbb {Z}\setminus \{0,\pm 1\}$ and $z\in \mathbb {Q}$.References
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Additional Information
- Tapani Matala-aho
- Affiliation: Department of Mathematical Sciences, University of Oulu, P. O. Box 3000, 90014 Oulu, Finland
- Email: tma@sun3.oulu.fi
- Keijo Väänänen
- Affiliation: Department of Mathematical Sciences, University of Oulu, P. O. Box 3000, 90014 Oulu, Finland
- Email: kvaanane@sun3.oulu.fi
- Wadim Zudilin
- Affiliation: Department of Mechanics and Mathematics, Moscow Lomonosov State University, Vorobiovy Gory, GSP-2, 119992 Moscow, Russia
- Email: wadim@ips.ras.ru
- Received by editor(s): June 16, 2004
- Received by editor(s) in revised form: March 10, 2005
- Published electronically: December 20, 2005
- Additional Notes: This work is supported by an Alexander von Humboldt research fellowship and partially supported by grant no. 03-01-00359 of the Russian Foundation for Basic Research
- © Copyright 2005 American Mathematical Society
- Journal: Math. Comp. 75 (2006), 879-889
- MSC (2000): Primary 11J82, 33D15
- DOI: https://doi.org/10.1090/S0025-5718-05-01812-0
- MathSciNet review: 2196997