2019/10/31 by Rahul Dalal
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebra over a field #Automorphic L-function #Automorphic form #Component (thermodynamics) #Euler's formula #Extension (predicate logic) #Finite Group Theory Research #Infinity #Langlands–Shahidi method #Mathematical analysis #Mathematics #Pure mathematics #Representation (politics) #Riemann hypothesis #Selberg trace formula #Series (stratigraphy) #Simple (philosophy) #TRACE (psycholinguistics) #math.NT #math.RT #msc:11F55 #msc:11F70 #msc:11F72 #msc:11F75 #msc:22E50 #msc:22E55
paper · pdf · doi:10.2140/ant.2022.16.59
published as Alg. Number Th. 16 (2022) 59-137 · 74 pages. Beyond lots of typo corrections, there were some material corrections in sections 2.1, 6.4, and 10.1. 10.1 in particular had parts that were dependent on a reference that has been found to have a gap
arxiv created 2020/12/06 · openalex publication_date 2022/02/22 · arxiv updated 2022/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In arXiv:1208.1945, Shin and Templier proved certain equidistribution bounds on local components of certain families of automorphic representations. We extend their weight-aspect results to families of automorphic representations where the Archimedean component is restricted to a single discrete-series representation instead of an entire L-packet. We do this by using a so-called "hyperendoscopy" version of the stable trace formula developed by Ferrari. The main technical difficulties are defining a version of hyperendoscopy that works for groups without simply connected derived subgroup and bounding the values of transfers of unramified functions. We also present an extension of Arthur's simple trace formula for test functions with Euler-Poincaré component at infinity to non-cuspidal groups since it does not seem to appear elsewhere in the literature.