On the geometric side of the Arthur trace formula for the symplectic group of rank 2

2013/10/02 by Werner Hoffmann, Satoshi Wakatsuki, Hoffmann, Werner +1
Mathematics · #11E45 #11F72 #11S90 (Primary) 11R42 #22E30 #22E35 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1310.0541

openalex publication_date 2013/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We study the non-semisimple terms in the geometric side of the Arthur trace formula for the split symplectic similitude group or the split symplectic group of rank 2 over any algebraic number field. In particular, we show that the coefficients of unipotent orbital integrals are expressed by the Dedekind zeta function, Hecke L-functions, and the Shintani zeta function for the space of binary quadratic forms.

Related

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• The trace formula and prehomogeneous vector spaces
• A simple trace formula for arithmetic groups
• The Shintani double zeta functions
• Sur certaines contributions unipotentes dans la formule des traces d'Arthur