Michael Farmer Evans

A converse theorem for degree 2 elements of the Selberg class with restricted gamma factor

In this talk I shall talk about a converse theorem for a family of L functions of degree 2 with gamma factor coming from a holomorphic cuspform. These L functions coincide with either those coming from a newform or a product of L functions arising from Dirichlet characters.

Our converse theorem requires some weak analytic data on the Euler factors, naturally appearing in the Selberg class. We also suppose that the twisted L functions satisfy expected functional equations of the right conductor and the Gamma factors are unchanged under twists.