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

2015106 10:00 
2015107 16:00
 Place
 Faculty of Science Building #3210

Speaker/Organizer
 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^2Lefschetz 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.