{"paper":{"title":"Shintani cocycles and vanishing order of $p$-adic Hecke $L$-series at $s=0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michael Spiess","submitted_at":"2012-03-30T00:17:48Z","abstract_excerpt":"Let $\\chi$ be a Hecke character of finite order of a totally real number field $F$. By using Hill's Shintani cocyle we provide a cohomological construction of the $p$-adic $L$-series $L_p(\\chi, s)$ associated to $\\chi$. This is used to show that $L_p(\\chi, s)$ has a trivial zero at $s=0$ of order at least equal to the number of places of $F$ above $p$ where the local component of $\\chi$ is trivial."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6689","kind":"arxiv","version":3},"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"}