Number Theory Seminar

Wednesday 2/12/03 3:30-4:30 PM in Hylan 1104:
Suzanne Caulk- "Explicit action of Hecke operators on Hilbert-Siegel modular forms"

ABSTRACT:

We develop an algorithm for determining an explicit set of coset representatives (indexed by lattices) for the action of the Hecke operators T(P) and T_j(P²) on Hilbert-Siegel modular forms of fixed degree and weight. We then evaluate the action of the Hecke operators on Fourier series. Since this evaluation yields incomplete character sums for T_j(P²), we complete these sums by replacing the operator with a linear combination of T_k(P²), 1 <= k <= j. In all cases, this yields a clean and simple description of the action on Fourier coefficients.