2020/06/23 by Patrick Delorme, Delorme, Patrick
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Mathematical Analysis and Transform Methods #Representation Theory (math.RT) #advanced mathematical theories #math.RT
paper · pdf · doi:10.48550/arxiv.2006.12893
33 pages. Minor changes, corrections of typo
openalex publication_date 2020/06/23 · arxiv created 2021/04/21 · arxiv updated 2021/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the Hilbert subspace of L2(G(F)\backslash G(\A)) generated by wave packets of Eisenstein series built from discrete series is the whole space. Together with the work of Lapid \citeL1, it achieves a proof of the spectral theorem of Langlands based on the work of Bernstein and Lapid \citeBL on the meromorphic continuation of Eisenstein series. I have to say that I was unable to complete the proof of an earlier version. Instead, I use truncation on compact sets, as Arthur did to prove the Local Trace Formula in \citeAlt.