Arthur packets are certain generalizations of L-packets. Arthur and several others constructed Arthur packets for classical groups. Following ideas of the work of Adams-Barbasch-Vogan on Archimedean groups, Cunningham et al. proposed a purely local way to construct Arthur packets for any algebraic reductive group over p-adic fields. In this talk, I will introduce Cunningham’s proposal using one example for the exceptional group G2. This is a joint work with Cunningham and Fiori.

Riemann zeta functions and Dirichlet L-functions are first several examples of L-functions. Automorphic L-functions are vast generalizations of these L-functions. In this talk, I will give a quick survey of these L-functions and some related topics, including our recent work on holomorphy of adjoint L-function for GL(3) joint with Joseph Hundley.