A converse theorem for $\Gamma_0(13)$
Number Theory
2007-05-23 v1
Abstract
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 . 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.
Cite
@article{arxiv.math/0601549,
title = {A converse theorem for $\Gamma_0(13)$},
author = {J. B. Conrey and David W. Farmer and B. E. Odgers and N. C. Snaith},
journal= {arXiv preprint arXiv:math/0601549},
year = {2007}
}
Comments
10 pages, LaTeX