Barnes zeta function

In mathematics, a Barnes zeta function is a generalization of the Riemann zeta function introduced by E. W. Barnes (1901).

It is further generalized by the Shintani zeta function.

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.

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