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Ratios of multiplicity moments, H_q (cumulant over factorial momentsK_q/F_q), have been observed to show an oscillatory behaviour with respect toorder, q. Recent studies of e^+e^- annihilations at LEP have shown, moreover,that the amplitude and oscillation length vary strongly with the jet resolutionparameter y_{cut}. We study the predictions of the perturbative QCD partoncascade assuming low non-perturbative cut-off (Q_0\sim \Lambda_{QCD}\sim few100 MeV) and derive the expectations as a function of the cms energy and jetresolution from threshold to very high energies. We consider numericalsolutions of the evolution equations of gluodynamics in Double Logarithmic andModified Leading Logarithmic Approximations (DLA,MLLA), as well as results froma parton MC with readjusted parameters. The main characteristics are obtainedin MLLA, while a more numerically accurate description is obtained by the MCmodel. A unified description of correlations between hadrons and correlationsbetween jets emerges, in particular for the transition region of small y_{cut}.Comment: 31 pages, 14 figure

QCD explanation of oscillating hadron and jet multiplicity moments