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Finiteness of p-Divisible Sets of Multiple Harmonic Sums

Jianqiang Zhao
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Abstract

\medskip\noindent\textbf{Résumé.} Soit $l$ un entier et $\ors=(s_1, \dots, s_l)$ une séquence d'entiers positifs. Dans ce document, nous étudierons les propriétés arithmétique de sommes harmoniques multiples $H(\ors; n)$, qui est le $n$-ème somme partielle de la valeur de la série multiple zeta $ζ(\ors)$. On conjecture que pour tout $\ors$ et de tous les premiers $p$, il n'y a que de nombreux finitely $p$-partie intégrante sommes $H(\ors,n)$. Ceci généralise une conjecture de Eswarathasan et Levine et Boyd pour la série harmonique. Nous fournissons beaucoup d'éléments de preuve pour cette conjecture générale ainsi que certaines heuristiques argument soutenir. Ce document fait suite à \emph{Wolstenholme Type Theorem for multiple harmonic sums}, Intl.\ J.\ of Number Theory \textbf{4}(1) (2008) 73-106.

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Jianqiang Zhao. 2010-08-13. Finiteness of p-Divisible Sets of Multiple Harmonic Sums. https://arxiv.org/abs/math/0303043

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