{"paper":{"title":"Cauchy Means of Dirichlet polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Michel Weber","submitted_at":"2014-12-25T11:37:25Z","abstract_excerpt":"We study Cauchy means of Dirichlet polynomials $$\\int_\\R \\Big|\\sum_{n=1}^N \\frac{1}{ n^{\\s+ ist}} \\Big|^{2q}\n  \\frac{\\dd t}{\\pi( t^2+1)}.$$\n  These integrals were investigated when $q=1,\\s= 1, s=1/2 $ by Wilf, using integral operator theory and Widom's eigenvalue estimates.\n  We show the optimality of some upper bounds obtained by Wilf. We also obtain new estimates for the case $q\\ge 1$, $\\s\\ge 0$ and $s>0$. We complete Wilf's approach by relating it with other approaches (having notably connection with Brownian motion), allowing simple proofs, and also prove new results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7812","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"}