Hilbert and Siegel Modular Forms: Tuesday Report
(N. Ryan and N. Skoruppa) Prepared Arnaud Jehanne's 27 icosahedral modular forms for uploading to the frg data base, computed the root numbers and zeroes of the associated L-functions, and uploaded everything (see http://sage.math.washington.edu/home/nathan/weight-1-icosahedral-forms). So there are 6750 zeroes!
(N. Skoruppa) Implemented a class SiegelModularForm( SageObject) (see http://www.nskoruppa.de/siegel-modular-forms.sage) providing basic functionalities of a Siegel modular form of degree 2. In particular, we can now compute the Igusa generators.
(C. Citro, N. Ryan) Started to port the multiplication SiegelModularForms._mult_( F) to Cython.
- (L. Demb\'el\'e) Computed the first Hilbert modular forms; gave coefficients up to norm 10 000.
- (N. Ryan) Computed the first eight zeros of the L-function attached to Hilbert modular forms (assuming we have the right approximate functional equation for HMFs)