A converse theorem for \(\Gamma_0(13)\)

A converse theorem for \(\Gamma_0(13)\)

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 \(\Gamma_0(13)\). The proof does not assume a functional equation for the twists of the Dirichlet series. The main new ingredie...

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Veröffentlicht in:arXiv.org 2006-01
Hauptverfasser: Conrey, J B, Farmer, David W, Odgers, B E, Snaith, N C
Format: Artikel
Sprache:eng
Schlagworte:
Dirichlet problem
Functional equations
Theorems
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Zusammenfassung: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 \(\Gamma_0(13)\). 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.
ISSN:2331-8422