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The production of D mesons in proton-proton collisions at the LHCb detectoris studied. We consider the single production of D^0, D^+, D^star, and D_s^+mesons and correlation spectra in the production of DbarD and DD pairs at thesqrt{S}=7 TeV and sqrt{S}=13 TeV. In case of the single D-meson production wecalculate differential cross sections over transverse momentum p_T while in thepair DbarD,DD-meson production the cross sections are calculated over theazimuthal angle difference, rapidity difference, invariant mass of the pair Mand over the p_T of the one meson from a pair. The cross sections are obtainedat the leading order of the parton Reggeization approach usingKimber-Martin-Ryskin unintegrated parton distribution functions in a proton. Todescribe the D-meson production we use universal scale-dependent c-quark andgluon fragmentation functions fitted to e^+e^- annihilation data from CERNLEP1. Our predictions find a good agreement with the LHCb Collaboration datawithin uncertainties and without free parameters.

Large-p_T production of D mesons at the LHCb in the parton Reggeization approach