| Author: | MATSUMOTO Kohji, TSUMURA Hirofumi |
| AMS Classification: | 40B05, 11M06, 33E20 |
| Keywords: | Dirichlet ![tex:L]() -functions, double ![tex: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 ![tex:\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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