{"paper":{"title":"Generalised root identities for zeta functions of curves over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV"],"primary_cat":"math.NT","authors_text":"Richard Stone","submitted_at":"2012-02-12T10:38:47Z","abstract_excerpt":"We consider generalised root identities for zeta functions of curves over finite fields, \\zeta_{k}, and compare with the corresponding analysis for the Riemann zeta function. We verify numerically that, as for \\zeta, the \\zeta_{k} do satisfy the generalised root identities and we investigate these in detail for the special cases of \\mu=0,-1\\:\\&\\:-2. Unlike for \\zeta, however, we show that in the setting of zeta functions of curves over finite fields the \\mu=-2 root identity is consistent with the Riemann hypothesis (RH) proved by Weil. Comparison of this analysis with the corresponding calcula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4351","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"}