@article{oai:nagoya.repo.nii.ac.jp:00017981, author = {Matsumoto, Kohji and Tsumura, Hirofumi}, issue = {5}, journal = {Annales de l'institut Fourier}, month = {}, note = {We define Witten multiple zeta-functions associated with semisimple Lie algebras sl(n), (n=2,3,...) of several complex variables, and prove the analytic continuation of them. These can be regarded as several variable generalizations of Witten zeta-functions defined by Zagier. In the case sl(4), we determine the singularities of this function. Furthermore we prove certain functional relations among this function, the Mordell-Tornheim double zeta-functions and the Riemann zeta-function. Using these relations, we prove new and non-trivial evaluation formulas for special values of this function at positive integers.}, pages = {1457--1504}, title = {On Witten multiple zeta-functions associated with semisimple Lie algebras I}, volume = {56}, year = {2006} }