GSP(4)-PERIOD PROBLEMS OVER A QUADRATIC FIELD EXTENSION

Abstract

This thesis focuses on the distinction problems for G(E)/G(F), where G=GL(2) or GSp(4) and E is a quadratic field extension over a number field or a p-adic local field F. We use the theta lift to compute the dimension of G(F)-invariant distributions on a smooth irreducible admissible representation \pi of G(E) when F is a local field. We also have a global result for G(E)/G(F) with the help of the regularised Siegel-Weil formula.