{"paper":{"title":"La variante infinit\\'esimale de la formule des traces de Jacquet-Rallis pour les groupes lin\\'eaires","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Micha{\\l} Zydor","submitted_at":"2013-10-07T00:06:22Z","abstract_excerpt":"We establish an infinitesimal version of the Jacquet-Rallis trace formula for general linear groups. Our formula is obtained by integrating a kernel truncated a la Arthur multiplied by the absolute value of the determinant to the power $s \\in \\mathbb{C}$. It has a geometric side which is a sum of distributions $I_{\\mathfrak{o}}(s, \\cdot)$ indexed by the invariants of the adjoint action of $\\mathrm{GL}_n(\\mathrm{F})$ on $\\mathfrak{gl}_{n+1}(\\mathrm{F})$ as well as a \"spectral side\" consisting of the Fourier transforms of the aforementioned distributions. We prove that the distributions $I_{\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1650","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}