A converse theorem for $Γ_0(13)$

Conrey, J. B.; Farmer, David W.; Odgers, B. E.; Snaith, N. C.

A converse theorem for $Γ_0(13)$

Authors

Description

We prove that a Dirichlet series with a functional equation and Euler product of a particular form can only arise from a holomorphic cusp form on the Hecke congruence group $Γ_0(13)$. The proof does not assume a functional equation for the twists of the Dirichlet series. The main new ingredient is a generalization of the familiar Weil's lemma that played a prominent role in previous converse theorems.
10 pages, LaTeX