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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 and Satoshi Wakatsuki

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

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Table of Contents


Chapters

  • Chapter 1. Introduction
  • Chapter 2. Preliminaries
  • Chapter 3. A formula of Labesse and Langlands
  • Chapter 4. Shintani zeta function for the space of binary quadratic forms
  • Chapter 5. Structure of $\mathrm GSp(2)$
  • Chapter 6. The geometric side of the trace formula for $\mathrm GSp(2)$
  • Chapter 7. The geometric side of the trace formula for $\mathrm Sp(2)$
  • Appendix A. The group $\mathrm GL(3)$
  • Appendix B. The group $\mathrm SL(3)$

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 over any algebraic number field. In particular, we express the global coefficients of unipotent orbital integrals in terms of Dedekind zeta functions, Hecke -functions, and the Shintani zeta function for the space of binary quadratic forms.

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