Finiteness of p-Divisible Sets of Multiple Harmonic Sums

Details Finiteness of p-Divisible Sets of Multiple Harmonic Sums Finiteness of p-Divisible Sets of Multiple Harmonic Sums

2003-03-04

arxiv.org/abs/math/0303043v7

Mathematics

Number Theory

19 pages, some typos are corrected

Scientific paper

\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\'ements de preuve pour cette conjecture g\'en\'erale ainsi que certaines heuristiques argument soutenir. Ce document fait suite \`a \emph{Wolstenholme Type Theorem for multiple harmonic sums}, Intl.\ J.\ of Number Theory \textbf{4}(1) (2008) 73-106.

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