{"paper":{"title":"Algebraicity of L-values for elliptic curves in a false Tate curve tower","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Thanasis Bouganis, Vladimir Dokchitser","submitted_at":"2005-09-23T17:19:43Z","abstract_excerpt":"Let $E$ be an elliptic curve over $Q$, and $\\tau$ an Artin representation over $Q$ that factors through the non-abelian extension $Q(\\sqrt[p^n]{m},\\mu_{p^n})/Q$, where $p$ is an odd prime and $n,m$ are positive integers. We show that $L(E,\\tau,1)$, the special value at $s=1$ of the $L$-function of the twist of $E$ by $\\tau$, divided by the classical transcendental period $\\Omega_{+}^{d^+}|\\Omega_{-}^{d^-}|\\epsilon(\\tau)$ is algebraic and Galois-equivariant, as predicted by Deligne's conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509566","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"}