{"paper":{"title":"The lambda invariants at CM points","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hongbo Yin, Peng Yu, Tonghai Yang","submitted_at":"2018-10-17T04:27:50Z","abstract_excerpt":"In the paper, we show that $\\lambda(z_1) -\\lambda(z_2)$, $\\lambda(z_1)$ and $1-\\lambda(z_1)$ are all Borcherds products in $X(2) \\times X(2)$. We then use the big CM value formula of Bruinier, Kudla, and Yang to give explicit factorization formulas for the norms of $\\lambda(\\frac{d+\\sqrt d}2)$, $1-\\lambda(\\frac{d+\\sqrt d}2)$, and $\\lambda(\\frac{d_1+\\sqrt{d_1}}2) -\\lambda(\\frac{d_2+\\sqrt{d_2}}2)$, with the latter under the condition $(d_1, d_2)=1$. Finally, we use these results to show that $\\lambda(\\frac{d+\\sqrt d}2)$ is always an algebraic integer and can be easily used to construct units in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07381","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":""},"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"}