{"paper":{"title":"Finiteness of p-Divisible Sets of Multiple Harmonic Sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Jianqiang Zhao","submitted_at":"2003-03-04T18:26:44Z","abstract_excerpt":"\\medskip\\noindent\\textbf{R\\'esum\\'e.} Soit $l$ un entier et $\\ors=(s_1, \\dots, s_l)$ une s\\'equence d'entiers positifs. Dans ce document, nous \\'etudierons les propri\\'et\\'es arithm\\'etique de sommes harmoniques multiples $H(\\ors; n)$, qui est le $n$-\\`eme somme partielle de la valeur de la s\\'erie multiple zeta $\\zeta(\\ors)$. On conjecture que pour tout $\\ors$ et de tous les premiers $p$, il n'y a que de nombreux finitely $p$-partie int\\'egrante sommes $H(\\ors,n)$. Ceci g\\'en\\'eralise une conjecture de Eswarathasan et Levine et Boyd pour la s\\'erie harmonique. Nous fournissons beaucoup d'\\'el"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0303043","kind":"arxiv","version":7},"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"}