Approximants de Padé des $q$-polylogarithmes

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We solve a Padé-type problem of approximating three specific functions simultaneously by $q$-analogues of polylogarithms, respectively by powers of the logarithm. This problem is intimately related to recent results of the authors and Wadim Zudilin ["Séries hypergéométriques basiques, fonction $q$-zêta et séries d'Eisenstein", J. Inst. Math. Jussieu (to appear)] on the dimension of the vector space generated by $q$-analogues of values of the Riemann zeta function at integers. We also show that our result can be considered as a $q$-analogue of a result of Stéphane Fischler and the second author [J. Math. Pures Appl. {\bf 82} (2003), 1369-1394].
10 pages, AmS-LaTeX

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Number Theory, Classical Analysis and ODEs, Primary 41A21; Secondary 33D15

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http://salesiana.dossiersoluciones.com/handle/123456789/213323

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0407191
 http://arxiv.org/abs/math/0407191
 in: "Diophantine Approximation - Festschrift for Wolfgang Schmidt," Developments in Mathematics, Vol. 16, R. Tichy, H.-P. Schlickewei, K. Schmidt, eds., Springer-Verlag, New York, 2008, pp. 221-230.

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