SPEAKER: Gonzalo Tornaria
Brandt modules, Shimura correspondence,
and the central values of twisted L-series
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.