q-Analogues of the Barnes multiple zeta functions

Yoshinori Yamasaki

Published 2004-12-03, updated 2005-03-08Version 3

In this paper, we introduce $q$-analogues of the Barnes multiple zeta functions. We show that these functions can be extended meromorphically to the whole plane, and moreover, tend to the Barnes multiple zeta functions when $q\uparrow 1$ for all complex numbers.