On smoothing singularities of elliptic orbital integrals on GL(n) and\n Beyond Endoscopy

2016/08/21 by Oscar E. González, Chung‐Hang Kwan, González, Oscar E. +7 · 1 citation
Mathematics · Medicine · #11F66 #11F72 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Autoimmune and Inflammatory Disorders #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1608.05938

openalex publication_date 2016/08/21 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Recent work of Altu ug continues the preliminary analysis of Langlands'\nBeyond Endoscopy proposal for GL(2) by removing the contribution of the\ntrivial representation to the trace formula using a Poisson summation formula.\nWe show that Altu ug's method of smoothing real elliptic orbital integrals by\nan approximate functional equation extends to GL(n). We also discuss the case\nof an arbitrary reductive group, and remaining obstructions for applying\nPoisson summation.\n

Cited by

• A note on Poisson summation for GL(2)

Related

• Beyond Endoscopy via the trace formula - II: Asymptotic expansions of Fourier transforms and bounds towards the Ramanujan conjecture
• Beyond endoscopy for GL₂ over ℚ with ramification 3: contribution of the elliptic part
• Beyond endoscopy for GL₂ over ℚ with ramification 1: Poisson summation
• Beyond Endoscopy via Poisson Summation for GL(2,K)
• Refinements of the trace formula for GL(2)