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

M Lee; Andrew R Booker; Michael Farmer M F Farmer-Evans

doi:10.1017/fms.2023.22

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

M Lee, Andrew R Booker, Michael Farmer M F Farmer-Evans

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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.

Original language	English
Article number	e26
Number of pages	10
Journal	Forum of Mathematics, Sigma
Volume	11
Early online date	31 Mar 2023
DOIs	https://doi.org/10.1017/fms.2023.22
Publication status	Published - 2023

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title = "An extension of Venkatesh's converse theorem to the Selberg class",

abstract = "We extend Venkatesh{\textquoteright}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.",

author = "M Lee and Booker, {Andrew R} and Farmer-Evans, {Michael Farmer M F}",

year = "2023",

doi = "10.1017/fms.2023.22",

language = "English",

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journal = "Forum of Mathematics, Sigma",

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publisher = "Cambridge University Press",

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T1 - An extension of Venkatesh's converse theorem to the Selberg class

AU - Lee, M

AU - Booker, Andrew R

AU - Farmer-Evans, Michael Farmer M F

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

U2 - 10.1017/fms.2023.22

DO - 10.1017/fms.2023.22

M3 - Article (Academic Journal)

SN - 2050-5094

VL - 11

JO - Forum of Mathematics, Sigma

JF - Forum of Mathematics, Sigma

M1 - e26

ER -

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

Abstract

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