9/28/2005

Ram Murty
Queen's University

Multiple Hurwitz zeta functions

After a brief review of the theory of multiple zeta values and zeta functions, we will discuss the multiple Hurwitz zeta function given by $$\zeta(s_1, s_2,..., s_r; x_1, x_2,..., x_r) = \sum_{n_1>n_2>\cdots >n_r\geq1} {1 \over (n_1+x_1)^{s_1} (n_2+x_2)^{s_2} \cdots (n_r+x_r)^{s_r}$$ and derive its meromorphic continuation as a function of $(s_1, ..., s_r)\in {\Bbb C}^r$. This is joint work with Kaneenika Sinha.