In mathematics the Petersson inner product is an inner product defined on the space of entire modular forms. It was introduced by the German mathematician Hans Petersson.
Contents
Definition
Let
The mapping
is called Petersson inner product, where
is a fundamental region of the modular group
is the hyperbolic volume form.
Properties
The integral is absolutely convergent and the Petersson inner product is a positive definite Hermitian form.
For the Hecke operators
This can be used to show that the space of cusp forms of level