Next-to-MLLA corrections to single inclusive kt-distributions and 2-particle correlations in a jet

35 pages and 39 figures. Comments, appendices, figures, references added. Version to appear in Phys. Rev. DInternational audienceThe hadronic kt-spectrum inside a high energy jet is determined including corrections of relative magnitude O{\sqrt{\alpha_s}} with respect to the Modified Leading Logarithmic Approximation (MLLA), in the limiting spectrum approximation (assuming an infrared cut-off Q0 =Lambda_{QCD}) and beyond Q_0\ne\Lambda_{QCD}. The results in the limiting spectrum approximation are found to be, after normalization, in impressive agreement with preliminary measurements by the CDF collaboration, unlike what occurs at MLLA, pointing out small overall non-perturbative contributions. Within the same framework, 2-particle correlations inside a jet are also predicted at NMLLA and compared to previous MLLA calculations