{"paper":{"title":"Generalized Riemann Hypothesis, Time Series and Normal Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th"],"primary_cat":"math.NT","authors_text":"Andr\\'e LeClair, Giuseppe Mussardo","submitted_at":"2018-09-17T12:36:15Z","abstract_excerpt":"$L$ functions based on Dirichlet characters are natural generalizations of the Riemann $\\zeta(s)$ function: they both have series representations and satisfy an Euler product representation, i.e. an infinite product taken over prime numbers. In this paper we address the Generalized Riemann Hypothesis relative to the non-trivial complex zeros of the Dirichlet $L$ functions by studying the possibility to enlarge the original domain of convergence of their Euler product. The feasibility of this analytic continuation is ruled by the asymptotic behavior in $N$ of the series $B_N = \\sum_{n=1}^N \\cos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06158","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"}