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Mod p structure of alternating and non-alternating multiple harmonic sums

Jianqiang Zhao (2011)

Journal de Théorie des Nombres de Bordeaux

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 p 2 . If one replaces the harmonic series by k 1 1 / n k for k even, then the modulus has to be changed from p 2 to just p . One may consider generalizations of this to multiple harmonic sums (MHS) and alternating multiple harmonic sums (AMHS) which are partial sums of multiple zeta value series and the alternating Euler sums, respectively. A lot of results along this direction...

Morphismes sturmiens et règles de Rauzy

Filippo Mignosi, Patrice Séébold (1993)

Journal de théorie des nombres de Bordeaux

Nous donnons une caractérisation complète de tous les morphismes binaires qui préservent les mots sturmiens et montrons que les mots infinis engendrés par ces morphismes sont rigides.

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