{"paper":{"title":"Vanishing of L-functions of elliptic curves over number fields","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.NT","authors_text":"Chantal David, Hershy Kisilevsky, Jack Fearnley","submitted_at":"2004-06-01T11:29:53Z","abstract_excerpt":"Let $E$ be an elliptic curve over $\\mathbb{Q}$, with L-function $L_E(s)$. For any primitive Dirichlet character $\\chi$, let $L_E(s, \\chi)$ be the L-function of $E$ twisted by $\\chi$. In this paper, we use random matrix theory to study vanishing of the twisted L-functions $L_E(s, \\chi)$ at the central value $s=1$. In particular, random matrix theory predicts that there are infinitely many characters of order 3 and 5 such that $L_E(1, \\chi)=0$, but that for any fixed prime $k \\geq 7$, there are only finitely many character of order $k$ such that $L_E(1, \\chi)$ vanishes. With the Birch and Swinne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0406012","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0406012/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}