Converse theorems and the grand simplicity hypothesis

In this talk, we will be interested in two manifestations of the so-called grand simplicity hypothesis for the zeros of automorphic L-functions. Specifically, we will see how the simplicity and independence of zeros can be related to the characterisation of automorphic L-functions in terms of analytic data. We will state two converse theorems in low degree and outline their proof in terms of the asymptotics of hypergeometric functions.