SPEAKER: Gonzalo Tornaria

TITLE: Brandt modules, Shimura correspondence, and the central values of twisted L-series

ABSTRACT: Let f be an eigenform of weight 2 and prime level. A method of Gross constructs, provided L(f,1) does not vanish, a modular form of weight 3/2 whose Fourier coefficients relate to the central values of the L-series of the imaginary quadratic twists of f, giving an explicit formula for such central values.

We will present joint work with Z. Mao and F. Rodriguez-Villegas which generalizes Gross's algorithm and formula to include the case L(f,1)=0, and to the case of the real quadratic twists of f.