On Shintani zeta functions for GL(2)
In this paper we consider an analogue of the zeta function for not necessarily prehomogeneous representations of GL(2) and compute some of the poles.
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arXiv subjects
Akihiko Yukie
Publications and source records attributed to Akihiko Yukie.
On the convergence of the zeta function for certain prehomogeneous vector spaces
Let (G,V) be an irreducible prehomogeneous vector space defined over a number field k, P in k[V] a relative invariant polynomial, and X a rational character of G such that P(gx)=X(g)P(x). Let V_k^{ss}={x \in V_k such that P(x) is not equal to 0}. For x in V_k^{ss}, let G_x be the stabilizer of x, and G_x^0 the connected component of 1 of G_x. We define L_0 to be the set of x in V_k^{ss} such that G_x^0 does not have a non-trivial rational character. We study the zeta function for (G,V).
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