In this thesis, we study automorphic forms of full level on the rank 2 real symplectic group Sp(2). The primary result is a proof of the meromorphic continuation and functional equation of the degree 4 L-function attached to such an automorphic form. The actual objects of study are automorphic distributions, which are certain distribution vectors of automorphic representations; in some cases, automorphic distributions may be interpreted more simply as boundary distributions of automorphic forms. We may view L-functions as being attached to automorphic distributions rather than automorphic forms.; We study automorphic distributions using Fourier analysis and the analytic techniques of Miller and Schmid. Under certain conditions, the L-function may be written as a Mellin transform of certain Fourier components of the automorphic distribution, and the meromorphic continuation and functional equation are proved by an argument analogous to Hecke's classical proof for L-functions of modular forms. Otherwise, the L-function may be expressed as a Rankin-Selberg pairing, and the meromorphic continuation and functional equation are then derived from corresponding properties of Eisenstein series.
展开▼
