{"paper":{"title":"Equality of Dedekind sums mod $8 \\mathbb{Z}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Emmanuel Tsukerman","submitted_at":"2015-01-15T00:47:14Z","abstract_excerpt":"Using a generalization due to Lerch [M. Lerch, Sur un th\\'{e}or\\`{e}me de Zolotarev. Bull. Intern. de l'Acad. Fran\\c{c}ois Joseph 3 (1896), 34-37] of a classical lemma of Zolotarev, employed in Zolotarev's proof of the law of quadratic reciprocity, we determine necessary and sufficient conditions for the difference of two Dedekind sums to be in $8\\mathbb{Z}$. These yield new necessary conditions for equality of two Dedekind sums. In addition, we resolve a conjecture of Girstmair [Girstmair, Congruences mod 4 for the alternating sum of the partial quotients, arXiv: 1501.00655]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03544","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"}