ANALYTIC CONTINUATION OF APOSTOL-VU MULTIPLE BALANCING ZETA FUNCTIONS

摘要

In this note we introduce Apostol-Vu multiple balancing zeta functions as where si (i = 1, 2, . . . , r+1) are complex variables. We study the analytic continuation of Apostol-Vu multiple balancing zeta functions of three variables and calculate a complete list of the residues corresponding to their respective poles. Further we examine the values of these zeta functions at negative integers.