Finiteness of p-Divisible Sets of Multiple Harmonic Sums∗
نویسنده
چکیده
Abstract. Let l be a positive integer and s = (s1, . . . , sl) be a sequence of positive integers. In this paper we shall study the arithmetic properties of multiple harmonic sum H(s;n) which is the n-th partial sum of multiple zeta value series ζ(s). We conjecture that for every s and every prime p there are only finitely many p-integral partial sums H(s;n). This generalizes a conjecture of Eswarathasan and Levine and Boyd for harmonic series. We provide a lot of evidence for this general conjecture and make some heuristic argument to support it. This paper can be regarded as a sequel to Wolstenholme Type Theorem for multiple harmonic sums, Intl. J. of Num. Thy. 4(1) (2008) 73-106.
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تاریخ انتشار 2008