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

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

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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Veröffentlicht in:Forum of mathematics. Sigma 2023-01, Vol.11, Article e26
Hauptverfasser: Booker, Andrew R., Farmer, Michael, Lee, Min
Format: Artikel
Sprache:eng
Schlagworte:
Hypotheses
Number Theory
Theorems
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Zusammenfassung: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.
ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2023.22