{"paper":{"title":"On explicit Fourier expansions of theta lifts to ${\\rm SO}(3,n+1)$ arising from elliptic newforms of level one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Henry H. Kim, Takuya Yamauchi","submitted_at":"2026-06-04T01:01:56Z","abstract_excerpt":"Using degenerate Whittaker functions and explicit computations of Eisenstein series, we obtain explicit formulas for the Fourier expansions of theta lifts to the special orthogonal group $G={\\rm SO}(3,n+1)$ over $\\mathbb{Q}$, where $n\\ge 3$ and $G$ splits at all finite places. The theta lifts in question are Hecke eigen, non-cuspidal, square-integrable automorphic forms of weight $l$ ($l\\ge n+2$, even), arising from elliptic newforms for $\\SL_2(\\Z)$ of weight $l-\\frac{n-2}{2}$ when $n$ is even and $2l-n+1$ when $n$ is odd."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05549","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/2606.05549/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"}