{"paper":{"title":"On the zeta function on the line Re(s) = 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Johan Andersson","submitted_at":"2012-07-18T10:55:06Z","abstract_excerpt":"We show the estimates \\inf_T \\int_T^{T+\\delta} |\\zeta(1+it)|^{-1} dt =e^{-\\gamma}/4 \\delta^2+ O(\\delta^4) and \\inf_T \\int_T^{T+\\delta} |\\zeta(1+it)| dt =e^{-\\gamma} \\pi^2/24 \\delta^2+ O(\\delta^4) as well as corresponding results for sup-norm, L^p-norm and other zeta-functions such as the Dirichlet L-functions and certain Rankin-Selberg L-functions. This improves on previous work of Balasubramanian and Ramachandra for small values of \\delta and we remark that it implies that the zeta-function is not universal on the line Re(s)=1. We also use recent results of Holowinsky (for Maass wave forms) a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4336","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"}