Shintani zeta function

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For the Shintani zeta function of a vector space, see Prehomogeneous vector space.

In mathematics, a Shintani zeta function or Shintani L-function is a generalization of the Riemann zeta function. They were first studied by Takuro Shintani (1976). They include Hurwitz zeta functions, Barnes zeta functions, and Witten zeta functions as special cases.


The Shintani zeta function of (s1, ..., sk) is given by

where each Lj is an inhomogeneous linear function of (n1, ... ,nm). The special case when k = 1 is the Barnes zeta function.