Méthodes probabilistes en théorie des nombres
The well-known Wolstenholme’s Theorem says that for every prime the -st partial sum of the harmonic series is congruent to modulo . If one replaces the harmonic series by for even, then the modulus has to be changed from to just . 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...
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.