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On the Geometric Side of the Arthur Trace Formula for the Symplectic Group of Rank 2
About this Title
Werner Hoffmann, Fakultät für Mathematik, Universität Bielefeld, 33615 Bielefeld, Germany and Satoshi Wakatsuki, Faculty of Mathematics and Physics, Institute of Science and Engineering, Kanazawa University, Kakumamachi, Kanazawa, Ishikawa, 920-1192, Japan
Publication: Memoirs of the American Mathematical Society
Publication Year:
2018; Volume 255, Number 1224
ISBNs: 978-1-4704-3102-0 (print); 978-1-4704-4825-7 (online)
DOI: https://doi.org/10.1090/memo/1224
Published electronically: August 1, 2018
MSC: Primary 11F72, 11S90; Secondary 11R42, 11E45, 22E30, 22E35
Table of Contents
Chapters
- 1. Introduction
- 2. Preliminaries
- 3. A formula of Labesse and Langlands
- 4. Shintani zeta function for the space of binary quadratic forms
- 5. Structure of $\mathrm {GSp(2)}$
- 6. The geometric side of the trace formula for $\mathrm {GSp(2)}$
- 7. The geometric side of the trace formula for $\mathrm {Sp(2)}$
- A. The group $\mathrm {GL(3)}$
- B. The group $\mathrm {SL(3)}$
Abstract
We 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, we 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.- Tsuneo Arakawa, Special values of $L$-functions associated with the space of quadratic forms and the representation of $\textrm {Sp}(2n,F_p)$ in the space of Siegel cusp forms, Automorphic forms and geometry of arithmetic varieties, Adv. Stud. Pure Math., vol. 15, Academic Press, Boston, MA, 1989, pp. 99–169. MR 1040607, DOI 10.2969/aspm/01510099
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