A converse theorem for Γ₀(13)
Conrey, J. B. · Farmer, David W. · Odgers, B. E. · Snaith, N. C.
Original · EN
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 Γ₀(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.
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