• Corpus ID: 119680994

A converse theorem for Gamma (0) (13)

@article{Conrey2006ACT,
  title={A converse theorem for Gamma (0) (13)},
  author={J. Brian Conrey and David W. Farmer and B. E. Odgers and Nina C. Snaith},
  journal={Journal of Number Theory},
  year={2006},
  pages={314-323}
}
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. 

References

SHOWING 1-6 OF 6 REFERENCES
An extension of Hecke's converse theorem
Associated to a newform $f(z)$ is a Dirichlet series $L_f(s)$ with functional equation and Euler product. Hecke showed that if the Dirichlet series $F(s)$ has a functional equation of the appropriate
On the structure of the Selberg class, I: 0≤d≤1
The Selberg class S is a rather general class of Dirichlet series with functional equation and Euler product and can be regarded as an axiomatic model for the global L-functions arising from number
Über die Riemannsche Funktionalgleichung der ζ-Funktion
On the structure of the Selberg class, V: 1 < d < 5/3