{"paper":{"title":"Higher Siegel--Weil formula for unitary groups II: corank one terms","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.NT","authors_text":"Benjamin Howard, Mikayel Mkrtchyan, Tony Feng","submitted_at":"2025-07-17T18:31:13Z","abstract_excerpt":"We prove the higher Siegel--Weil formula for \\emph{corank one} terms, relating (1) the $r^{\\rm th}$ central derivatives of corank one Fourier coefficients of Siegel--Eisenstein series, and (2) the degrees of special cycles of virtual dimension 0 on the moduli stack of Hermitian shtukas with $r$ legs. Notably, the formula holds for all $r$, regardless of the order of vanishing of the Eisenstein series. This extends earlier work of Feng--Yun--Zhang, who proved the higher Siegel--Weil formula for the non-singular (corank zero) terms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13473","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.13473/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}