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math.NT2022
An extension of Venkatesh's converse theorem to the Selberg class
Andrew R. Booker, Michael Farmer, Min Lee
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,…
math.NT2021
A converse theorem for degree 2 elements of the Selberg class with restricted gamma factor
Michael Farmer
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 comin…
math.NT2021
Strong multiplicity one for the Selberg class
Michael Farmer
We study the problem of determining elements of the Selberg class by information on the coefficents of the Dirichlet series at the squares of primes, or information about the zeroe…