On the Geometric Side of the Arthur Trace Formula for the Symplectic Group of Rank 2 (Memoirs of the American Mathematical Society)

Hoffmann, Werner/ Wakatsuki, Satoshi

American Mathematical Society（2018/08発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 88 p.
• 言語 ENG
• 商品コード 9781470431020
• DDC分類 512.482

Full Description

The authors study the non-semisimple terms in the geometric side of the Arthur trace formula for the split symplectic similitude group and the split symplectic group of rank $2$ over any algebraic number field. In particular, they express the global coefficients of unipotent orbital integrals in terms of Dedekind zeta functions, Hecke $L$-functions, and the Shintani zeta function for the space of binary quadratic forms.

Contents

Introduction
Preliminaries
A formula of Labesse and Langlands
Shintani zeta function for the space of binary quadratic forms
Structure of $\mathrm{GSp}(2)$
The geometric side of the trace formula for $\mathrm{GSp}(2)$
The geometric side of the trace formula for $\mathrm{Sp}(2)$
Appendix A. The group $\mathrm{GL}(3)$
Appendix B. The group $\mathrm{SL}(3)$
References