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

2022/07/01 by Booker, Andrew R., Farmer, Michael, Lee, Min
#11M36 #11M41 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2207.00451

Abstract

We extend Venkatesh's proof of the converse theorem for classical holomorphic modular forms to arbitrary level and character. The method of proof, via the Petersson trace formula, allows us to treat arbitrary degree 2 gamma factors of Selberg class type.

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