{"paper":{"title":"The multiplicative Hilbert matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.NT"],"primary_cat":"math.FA","authors_text":"Aristomenis G. Siskakis, Dragan Vukoti\\'c, Karl-Mikael Perfekt, Kristian Seip, Ole Fredrik Brevig","submitted_at":"2014-11-26T16:42:17Z","abstract_excerpt":"It is observed that the infinite matrix with entries $(\\sqrt{mn}\\log (mn))^{-1}$ for $m, n\\ge 2$ appears as the matrix of the integral operator $\\mathbf{H}f(s):=\\int_{1/2}^{+\\infty}f(w)(\\zeta(w+s)-1)dw$ with respect to the basis $(n^{-s})_{n\\ge 2}$; here $\\zeta(s)$ is the Riemann zeta function and $H$ is defined on the Hilbert space ${\\mathcal H}^2_0$ of Dirichlet series vanishing at $+\\infty$ and with square-summable coefficients. This infinite matrix defines a multiplicative Hankel operator according to Helson's terminology or, alternatively, it can be viewed as a bona fide (small) Hankel op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7294","kind":"arxiv","version":3},"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"}