Reciprocity for $L$-functions twisted by Dirichlet characters

Reciprocity in the context of $L$-functions refers to a relation between
a moment of $L$-functions and a dual moment in a way that swaps
the roles of certain key parameters on both sides. In this talk I will discuss
reciprocity for the first moment of $GL(2)$ $L$-functions twisted by Dirichlet
characters.