Functional relations among certain double polylogarithms and their character analogues

Authors:

Kohji MATSUMOTO, Hirofumi TSUMURA

AMS Classification:

40B05, 11M06, 33E20

Keywords:

Dirichlet L-functions, double L-series, double zeta values, Mordell-Tornheim double zeta-functions, Riemann zeta-function, polylogarithms

Abstract:

In this paper, we consider certain double polylogarithms and the ordinary polylogarithm of complex variables, and introduce a method of producing functional relations among them. Furthermore we consider \chi-analogues of them. These functional relations can be regarded as polylogarithmic generalizations of the known relations between the Mordell-Tornheim double zeta-function and the Riemann zeta-function, and their character analogues, which were studied by the authors.

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matsumoto&tsumura-08.pdf

Vol. 3 (11), 2008