Regularized Peterson inner products

We develop a regularization for Petersson inner products for arbitrary weakly
holomorphic and meromorphic modular forms. As applications, we extend for
of Duke, Imamoglu and Torth on regularized inner products of weakly holomorphic
modular forms of  weights 0 and 3/2, motivate a Hecke structure for weakly
holomorphic modular forms and write specializations of Greens functions as
inner product.