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 newline newline