# An extension of Venkatesh's converse theorem to the Selberg class

Speaker: Min Lee

Date: Fri, Jul 29, 2022

Conference: Moments of L-functions Workshop

Subject:

Class: Scientific

### Abstract:

In his thesis, Venkatesh gave a new proof of the classical converse theorem for modular forms of level~$1$ in the context of Langlands' Beyond Endoscopy". We extend his approach to arbitrary levels and characters. The method of proof, via the Petersson trace formula, allows us to treat arbitrary degree~$2$ gamma factors of Selberg class type.
This is joint work with Andrew R. Booker and Michael Farmer.