{"paper":{"title":"On generalized Li criterion for a certain class of $L-$functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Almasa Od\\v{z}ak, Anne-Maria Ernvall-Hyt\\\"onen, Lejla Smajlovi\\'c, Medina Su\\v{s}i\\'c","submitted_at":"2014-10-16T11:58:00Z","abstract_excerpt":"We define generalized Li coefficients, called $\\tau-$Li coefficients for a very broad class $\\mathcal{S}^{\\sharp \\flat }(\\sigma_0, \\sigma_1)$ of $L-$functions that contains the Selberg class, the class of all automorphic $L-$functions and the Rankin-Selberg $L-$functions, as well as products of suitable shifts of those functions. We prove the generalized Li criterion for zero-free regions of functions belonging to the class $\\mathcal{S}^{\\sharp \\flat }(\\sigma_0, \\sigma_1)$, derive an arithmetic formula for the computation of $\\tau-$Li coefficients and conduct numerical investigation of $\\tau-$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4384","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"}