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

2021/10/01 by Farmer, Michael
#11M36 #11M41 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2110.00311

Abstract

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 don't require anything on the shape. We also suppose that the twisted L functions satisfy expected functional equations. We allow the non-trivial twists to have arbitrary poles.

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