Barnes zeta function
In mathematics, a Barnes zeta function is a generalization of the Riemann zeta function introduced by. It is further generalized by the Shintani zeta function.Definition
The Barnes zeta function is defined by
where w and aj have positive real part and s has real part greater than N.
It has a meromorphic continuation to all complex s, whose only singularities are simple poles at s = 1, 2,..., N. For N = w = a1 = 1 it is the Riemann zeta function.
