Mod p structure of alternating and non-alternating multiple harmonic sums
نویسندگان
چکیده
منابع مشابه
Mod p structure of alternating and non-alternating multiple harmonic sums
The well-known Wolstenholme’s Theorem says that for every prime p > 3 the (p−1)-st partial sum of the harmonic series is congruent to 0 modulo p2. If one replaces the harmonic series by ∑ k≥1 1/n for k even, then the modulus has to be changed from p2 to just p. One may consider generalizations of this to multiple harmonic sums (MHS) and alternating multiple harmonic sums (AMHS) which are partia...
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By convention we set H(s;n) = 0 any n < d. We call l(s) := d and |s| := ∑d i=1 |si| its depth and weight, respectively. We point out that l(s) is sometimes called length in the literature. When every si is positive we recover the multiple harmonic sums (MHS for short) whose congruence properties are studied in [9, 10, 17, 18]. There is another “non-strict” version of the AMHS defined as follows...
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2011
ISSN: 1246-7405
DOI: 10.5802/jtnb.762