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

Published online by Cambridge University Press:  22 January 2016

Akihiko Yukie
Akihiko Yukie*
Affiliation:
Mathematics Department, College of Arts and Sciences, Oklahoma State University, Stillwater OK 74078, USA
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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 measure.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 140 , December 1995 , pp. 1 - 31
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1995

References

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