A converse theorem for degree 2 elements of the Selberg class with restricted gamma factor
Tom 205 / 2022
Streszczenie
We prove a converse theorem for a family of L-functions of degree 2 with gamma factor coming from a holomorphic cuspform. We show these L-functions coincide with either those coming from a newform or a product of L-functions arising from Dirichlet characters. We require some analytic data on the Euler factors, but do not require anything on the shape. We also suppose that the twisted L-functions satisfy expected functional equations. We incorporate the ideas from a 2014 paper by Booker and Krishnamurthy so that the non-trivial twists are allowed to have arbitrary poles.