Multiple zeta-functions associated with linear recurrence sequences and the vectorial sum formula.
Résumé
We prove the holomorphic continuation of certain multi-variable multiple zeta-functions whose coefficients satisfy a suitable recurrence condition. Actually we introduce more general vectorial zeta-functions, and prove their holomorphic continuation. Moreover we show a vectorial sum formula among those vectorial zeta-functions, from which some generalizations of the classical sum formula can be deduced.