{"paper":{"title":"Dedekind Sums with Even Denominators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michael Kural","submitted_at":"2018-01-01T21:49:49Z","abstract_excerpt":"Let $S(a,b)$ denote the normalized Dedekind sum. We study the range of possible values for $S(a,b)=\\frac{k}{q}$ with $\\gcd(k,q)=1$. Girstmair proved local restrictions on $k$ depending on $q\\pmod{12}$ and whether $q$ is a square and conjectured that these are the only restrictions possible. We verify the conjecture in the cases $q$ even, $q$ a square divisible by $3$ or $5$, and $2\\le q\\le 200$ (the latter by computer), and provide progress towards a general approach."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00517","kind":"arxiv","version":2},"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"}