We study some methods on generalized relative invariant distributions of p-adic groups. We establish the generalized Frobenius reciprocity and its derived version for p-adic groups. As a consequence, we completely describe the space of generalized relative invariant distributions on homogeneous space, and give
a criteria of automatic extension of generalized relative invariant distributions
on the space with finitely many orbits.
Based on the meromorphic continuation of zeta integral on varieties, we give another criteria with purely algebraic geometric conditions, on the extension of generalized relative invariant distributions , which can be viewed as a generalization of Tate thesis at local field. This talk is based on the joint work with Binyong Sun.