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

Linfoot Number Theory Seminar

10th November 2021, 11:00 am – 12:00 pm

Fry Building, Room LG.20

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.

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