Automorphic Forms and L-functions for Symplectic Groups of Genus 3

Abstract

For the similitude symplectic group GSp_6 over a totally real number field F, we establish the meromorphic continuation of the standard L-function and the spin L-function which are Langlands L-functions associated to the automorphic representation of PGSp_6 (A_F). In the second part of this thesis we compute the dimesion of the spaces of automorphic forms for rank 3 unitary groups where the entries of the group are from a definite quaternion algebra B over Q. This group is an inner form of GSp_6 over Q.