we will discuss questions surrounding automorphic l-functions, particularly deligne’s conjecture about critical values of motivic l-functions. in particular, we study the adjoint l-function of u(2,1).

hundley showed that a certain integral, involving an eisenstein series on the exceptional group g_2, computes this l-function at unramified places. we discuss the computation of this integral at the archimedean place for quaternionic modular forms, and how this relates to deligne's
conjecture.