Speaker: 若槻 聡，金沢大学 Inviter: 李文威 博士 Title: On coefficients of unipotent orbital integrals for the symplectic group of rank 2 Time & Venue: 2013.5.15 2:00pm C610 Abstract: This is a joint work with Werner Hoffmann. The geometric side of the Arthur trace formula is expressed as a linear combination of weighted orbital integrals. In the expansion, coefficients of unipotent orbital integrals are not understood in general. First, we review known results on coefficients for GL(2) and SL(2). In such the cases, the coefficients are expressed by the constant term of the Laurent expansion of the Dedekind zeta function at s=1 and the special values of Hecke L-functions at s=1. Especially, the coefficients for SL(2) are closely related to Hirzebruch's signature defect. Next, we mention our main result on coefficients of unipotent orbital integrals for the symplectic group of rank 2. We show that the coefficients are expressed by the constant term of the Laurent expansion of the Shintani zeta function for the space of binary quadratic forms at s=3/2 in addition to the Dedekind zeta function and Hecke L-functions. Furthermore, we explain relations between these results and stabilization.
