Christian Krattenthaler and Tanguy Rivoal

Approximants de Padé des q-polylogarithmes

(10 pages)

English Abstract. We solve a Padé-type problem of approximating three specific functions simultaneously by q-analogues of polylogarithms, respectively by powers of the logarithm. This approximation prolem 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. Our result can be considered as a q-analogue of a result of Stephane Fischler and the second author [J. Math. Pures Appl. 82 (2003), 1369-1394].

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