The Gindikin-Karpelevich Formula and Constant Terms of Eisenstein Series for Brylinski-Deligne Extensions

Abstract

In this dissertation the author firstly studies the L-group constructed by M. Weissman for Brylinski-Deligne (BD) extensions, including the splitting properties. Secondly, a refined Gindikin-Karpelevich formula is obtained and interpreted on the L-group side as Langlands-Shahidi type L-functions, based on the previous study of the L-group. In the end, the residual spectrum of some semisimple rank-one BD covers are determined and open problems for further investigation are discussed.