Seminar on Algebraic Geometry:Dimension formulas for spaces of Siegel modular forms

2015-10-6 10:00 - 2015-10-7 16:00
Faculty of Science Building #3-210
Satoshi Wakatsuki (Kanazawa University)
In this talk, we report explicit formulas for dimensions of spaces of holomorphic Siegel cusp forms.

First, we explain Godement's formula which expresses the dimensions by an integration of reproducing kernels.
Next, we introduce Shintani zeta functions for spaces of symmetric matrices.
Using Godement's formula, we can relate the dimensions to special values of Shintani zeta functions.
A sum of multiplicities of some discrete series can be calculated in principle by Arthur's L^2-Lefschetz trace formula. By an explanation of this formula, we will show what is needed in general to calculate dimensions of spaces of holomorphic cusp forms (multiplicities of holomorphic discrete series).

Finally, we give some results about explicit dimension formulas.