{"paper":{"title":"Simultaneous nonvanishing of Dirichlet $L$-functions in Galois orbits","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandra Florea, Hieu T. Ngo, Hung M. Bui","submitted_at":"2025-07-09T07:27:42Z","abstract_excerpt":"Under the Generalized Riemann Hypothesis, we prove that given any two distinct imprimitive Dirichlet characters $\\eta_1, \\eta_2$ modulo $q=p^k$, a positive proportion of characters $\\chi$ modulo $q$ in a fixed Galois orbit of primitive characters satisfies the nonvanishing property that $L(1/2,\\chi \\eta_1) L(1/2,\\chi \\eta_2) \\neq 0$, as $k \\to \\infty$ (with $p$ fixed). Previously, only a positive proportion of nonvanishing result was available in Galois orbits (as opposed to simultaneously nonvanishing), due to work of Khan, Mili\\'cevi\\'c and Ngo. The main ingredients are obtaining a sharp upp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.06609","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/2507.06609/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"}