{"paper":{"title":"On relations equivalent to the generalized Riemann hypothesis for the Selberg class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kamel Mazhouda, Lejla Smajlovi\\'c","submitted_at":"2015-11-14T19:31:57Z","abstract_excerpt":"In this paper we prove that the Generalized Riemann Hypothesis (GRH) for functions in the class $\\mathcal{S}^{\\sharp\\flat}$ containing the Selberg class is equivalent to a certain integral expression of the real part of the generalized Li coefficient $\\lambda_F(n)$ associated to $F\\in\\mathcal{S}^{\\sharp\\flat}$, for positive integers $n$. Moreover, we deduce that the GRH is equivalent to a certain expression of $Re(\\lambda_F(n))$ in terms of the sum of the Chebyshev polynomials of the first kind. Then, we partially evaluate the integral expression and deduce further relations equivalent to the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04603","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"}