### Publication Type:

Thesis
### Source:

Mathematics and Statistics, McGill University, p.79 (1997)
### Abstract:

Let f be a cusp form of weight 2 and level N. Let K be an imaginary quadratic field of discriminant - D, and d an ideal class of K. We obtain precise formulas for the special values of the L-functions associated to the Rankin convolution off and a theta series associated to the ideal class A, in
terms of the Petersson scalar product of f with the theta series associated to an Eichler order in a positive definite quaternion algebra. Our work is an extension of the work done by Gross [7] il. The central tools used in this thesis are Rankin's method and a reformulation of Gross of work of Waldspurger concerning central critical values.