An extension of Hecke's converse theorem

Details An extension of Hecke's converse theorem An extension of Hecke's converse theorem

1995-02-22

arxiv.org/abs/math/9502209v1

Mathematics

Number Theory

Scientific paper

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 form, then $F(s)=L_f(s)$ for some holomorphic newform $f(z)$ on $\Gamma(1)$. Weil extended this result to $\Gamma_0(N)$ under an assumption on the twists of $F(s)$ by Dirichlet characters. We show that, at least for small $N$, the assumption on twists can be replaced by an assumption on the local factors of the Euler product of $F(s)$.

Affiliated with

Also associated with

No associations

Rating

An extension of Hecke's converse theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An extension of Hecke's converse theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An extension of Hecke's converse theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-30404