Abstract: We consider zeta integrals (zeta distributions) associated
to a prehomogeneous space. Zeta integrals are useful tools
to study zeta functions in number theory, and it is closely
related to the representation theory of real Lie groups.
In this talk, we give a brief survey on zeta integrals
including the basics of the theory of prehomogeneous vector
spaces. In the latter half of the talk, we concentrate on
the prehomogeneous vector space called "enhanced symmetric
space". We pick a positive cone and study the zeta integral
over the cone. We will discuss its meromorphic continuation
and Fourier transform.
This is an on-going joint work with Bent Ørsted (Aarhus
Univ.) and Akihito Wachi (Hokkaido Univ. of Education).
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