On the convergence of the zeta function for certain prehomogeneous vector spaces

  title={On the convergence of the zeta function for certain prehomogeneous vector spaces},
  author={Akihiko Yukie},
  journal={Nagoya Mathematical Journal},
  pages={1 - 31}
  • Akihiko Yukie
  • Published 15 August 1994
  • Mathematics
  • Nagoya Mathematical Journal
Let (G, V) be an irreducible prehomogeneous vector space defined over a number field k, P ∈ k[V] a relative invariant polynomial, and χ a rational character of G such that . For , let Gx be the stabilizer of x, and the connected component of 1 of Gx . We define L0 to be the set of such that does not have a non-trivial rational character. Then we define the zeta function for (G, Y) by the following integral where Φ is a Schwartz-Bruhat function, s is a complex variable, and dg” is an invariant… 

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