{"paper":{"title":"Resultantal varieties related to zeroes of L-functions of Carlitz modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandr N. Grishkov, Dmitry Logachev","submitted_at":"2012-05-13T19:05:43Z","abstract_excerpt":"We show that there exists a connection between two types of objects: some kind of resultantal varieties over C, from one side, and varieties of twists of the tensor powers of the Carlitz module such that the order of 0 of its L-functions at infinity is a constant, from another side. Obtained results are only a starting point of a general theory. We can expect that it will be possible to prove that the order of 0 of these L-functions at 1 (i.e. the analytic rank of a twist) is not bounded --- this is the function field case analog of the famous conjecture on non-boundedness of rank of twists of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2900","kind":"arxiv","version":7},"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"}