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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