{"paper":{"title":"The Igusa modular forms and ``the simplest'' Lorentzian Kac--Moody algebras","license":"","headline":"","cross_cats":["hep-th","math.AG","math.QA","q-alg"],"primary_cat":"alg-geom","authors_text":"Valeri A. Gritsenko, Viacheslav V. Nikulin","submitted_at":"1996-03-13T21:34:45Z","abstract_excerpt":"We find automorphic corrections for the Lorentzian Kac--Moody algebras with the simplest generalized Cartan matrices of rank 3:\n  A_{1,0} =\n  2 0 -1\n  0 2 -2\n  -1 -2 2\n  and\n  A_{1,I} =\n  2 -2 -1\n  -2 2 -1\n  -1 -1 2\n  For A_{1,0} this correction is given by the Igusa Sp_4(Z)-modular form \\chi_{35} of weight 35, and for A_{1,I} by a Siege modular form of weight 30 with respect to a 2-congruence subgroup. We find infinite product or sum expansions for these forms. Our method of construction of \\chi_{35} leads to the direct construction of Siegel modular forms by infinite product expansions, whos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9603010","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"}