Approximants de Pad\'e des $q$-polylogarithmes
数论
2008-12-23 v1 经典分析与常微分方程
摘要
We solve a Pad\'e-type problem of approximating three specific functions simultaneously by -analogues of polylogarithms, respectively by powers of the logarithm. This problem is intimately related to recent results of the authors and Wadim Zudilin ["S\'eries hyperg\'eom\'etriques basiques, fonction -z\^eta et s\'eries d'Eisenstein", J. Inst. Math. Jussieu (to appear)] on the dimension of the vector space generated by -analogues of values of the Riemann zeta function at integers. We also show that our result can be considered as a -analogue of a result of St\'ephane Fischler and the second author [J. Math. Pures Appl. {\bf 82} (2003), 1369-1394].
引用
@article{arxiv.math/0407191,
title = {Approximants de Pad\'e des $q$-polylogarithmes},
author = {Christian Krattenthaler and Tanguy Rivoal},
journal= {arXiv preprint arXiv:math/0407191},
year = {2008}
}
备注
10 pages, AmS-LaTeX