{"paper":{"title":"A ring of symmetric Hermitian modular forms of degree $2$ with integral Fourier coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Toshiyuki Kikuta","submitted_at":"2019-03-28T15:09:01Z","abstract_excerpt":"We determine the structure over $\\mathbb{Z}$ of the ring of symmetric Hermitian modular forms with respect to $\\mathbb{Q}(\\sqrt{-1})$ of degree $2$ (with a character), whose Fourier coefficients are integers. Namely, we give a set of generators consisting of $24$ modular forms. As an application of our structure theorem, we give the Sturm bounds of such the modular forms of weight $k$ with $4\\mid k$, in the case $p=2$, $3$. We remark that the bounds for $p\\ge 5$ are already known."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.12036","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"}