4 papers
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,…
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…
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…
Quantitative recurrence properties for self-conformal sets
Simon Baker, Michael Farmer
In this paper we study the quantitative recurrence properties of self-conformal sets equipped with the map induced by the left shift. In particular, given a function…