Shintani zeta function
Encyclopedia
In mathematics, a Shintani zeta function or Shintani L-function is a generalization of the Riemann zeta function. They were studied studied by . They include Hurwitz zeta functions, Barnes zeta function
s, and Witten zeta function
s as special cases.
where each Lj is an inhomogeneous linear function of (n1, ... ,nm). The special case when k = 1 is the Barnes zeta function
.
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...
s, and Witten zeta function
Witten zeta function
In mathematics, the Witten zeta function, introduced by , is a function associated to a root system that encodes the degrees of the irreducible representations of the corresponding Lie group...
s as special cases.
Definition
The Shintani zeta function of (s1, ..., sk) is given bywhere each Lj is an inhomogeneous linear function of (n1, ... ,nm). The special case when k = 1 is the Barnes zeta function
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...
.