{"paper":{"title":"On the Gross-Stark Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kevin Ventullo, Mahesh Kakde, Samit Dasgupta","submitted_at":"2016-05-26T07:12:18Z","abstract_excerpt":"In 1980, Gross conjectured a formula for the expected leading term at $s=0$ of the Deligne--Ribet $p$-adic $L$-function associated to a totally even character $\\psi$ of a totally real field $F$. The conjecture states that after scaling by $L(\\psi \\omega^{-1}, 0)$, this value is equal to a $p$-adic regulator of units in the abelian extension of $F$ cut out by $\\psi \\omega^{-1}$. In this paper, we prove Gross's conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08169","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"}