Download or read book Local Zeta Functions Attached to the Minimal Spherical Series for a Class of Symmetric Spaces written by Nicole Bopp and published by American Mathematical Soc.. This book was released on 2005 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this paper is to prove a functional equation for a local zeta function attached to the minimal spherical series for a class of real reductive symmetric spaces. These symmetric spaces are obtained as follows. We consider a graded simple real Lie algebra $\widetilde{\mathfrak g}$ of the form $\widetilde{\mathfrak g}=V^-\oplus \mathfrak g\oplus V^+$, where $[\mathfrak g,V^+]\subset V^+$, $[\mathfrak g,V^-]\subset V^-$ and $[V^-,V^+]\subset \mathfrak g$. If the graded algebra is regular, then a suitable group $G$ with Lie algebra $\mathfrak g$ has a finite number of open orbits in $V^+$, each of them is a realization of a symmetric space $G\slash H_p$.The functional equation gives a matrix relation between the local zeta functions associated to $H_p$-invariant distributions vectors for the same minimal spherical representation of $G$. This is a generalization of the functional equation obtained by Godement} and Jacquet for the local zeta function attached to a coefficient of a representation of $GL(n,\mathbb R)$.