Functions l – Modular forms and period polynomials.

1.) What is the importance of the special values ​​of the L functions in relation to the weakly holomorphic modular forms? Why the study of special values ​​is a subject of intense study, except the fact that it is useful for some important conjectures?

2.) How can we prove that the special values ​​of the L functions correspond to the coefficients of the period polynomials in the case of holomorphic and weakly holomorphic modular forms?