Approximants de Padé des $q$-polylogarithmes

Details Approximants de Padé des $q$-polylogarithmes Approximants de Padé des $q$-polylogarithmes

2004-07-12

arxiv.org/abs/math/0407191v1

in: "Diophantine Approximation - Festschrift for Wolfgang Schmidt," Developments in Mathematics, Vol. 16, R. Tichy, H.-P. Schl

Mathematics

Number Theory

10 pages, AmS-LaTeX

Scientific paper

We solve a Pad\'e-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 ["S\'eries hyperg\'eom\'etriques basiques, fonction $q$-z\^eta et s\'eries 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 St\'ephane Fischler and the second author [J. Math. Pures Appl. {\bf 82} (2003), 1369-1394].

Affiliated with

Also associated with

No associations

Rating

Approximants de Padé des $q$-polylogarithmes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Approximants de Padé des $q$-polylogarithmes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Approximants de Padé des $q$-polylogarithmes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-58363