Modular forms, quaternion algebras, and special values of L-functions

Publication Type:

Thesis

Authors:

Daghigh, H.

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.

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