Values at non-positive integers of generalized Euler–Zagier multiple zeta-functions

摘要

We give new closed and explicit formulas for special values at non-positiveinteger points of generalized Euler-Zagier multiple zeta-functions and itspartially twisted analogues. In the non-twisted case, we first prove theseformulas for a small convenient class of these multiple zeta-functions and thenuse the analyticity of the values on the parameters defining the multiplezeta-functions to deduce the formulas in the general case. Also, for our aim weprove an extension of "Raabe's lemma" due to E. Friedman and A. Pereira. In thepartially twisted case, we use a different method based on M. de Crisenoy'sresult on the fully twisted case and the Mellin-Barnes integral formula.