Geodesic
An extension of Venkatesh’s converse theorem to the Selberg class
Forum of Mathematics, Sigma, Tome 11 (2023)

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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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     title = {An extension of {Venkatesh{\textquoteright}s} converse theorem to the {Selberg} class},
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Andrew R. Booker; Michael Farmer; Min Lee. An extension of Venkatesh’s converse theorem to the Selberg class. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.22

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