{"paper":{"title":"The first non-vanishing quadratic twist of an automorphic L-series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alex Kontorovich, Jeff Hoffstein","submitted_at":"2010-08-04T18:37:45Z","abstract_excerpt":"Let pi be an automorphic representation on GL(r, A_Q) for r=1, 2, or 3. Let d be a fundamental discriminant and chi_d the corresponding quadratic Dirichlet character. We consider the question of the least d, relative to the data (level, weight or eigenvalue) of pi, such that the central value of the twisted L-series is nonzero, i.e. L(1/2, pi x chi_d) != 0. For example, let N be the level of pi. Using multiple Dirichlet series, we prove the nonvanishing of a central twisted $L$-value with d << N^{1/2} for GL(1), d << N^1 for GL(2), and d << N^2 for GL(3), the last case assuming that a certain "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0839","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"}