Majorations de fonctions arithmétiques en moyenne sur des ensembles de faible densité
We consider minimal redundant digit expansions in canonical number systems in the gaussian integers. In contrast to the case of rational integers, where the knowledge of the two least significant digits in the “standard” expansion suffices to calculate the least significant digit in a minimal redundant expansion, such a property does not hold in the gaussian numbers : We prove that there exist pairs of numbers whose non-redundant expansions agree arbitrarily well but which have different least significant...
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...