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Using information from the marginality conditions of vertex operators for theAdS_5 x S^5 superstring, we determine the structure of the dependence of theenergy of quantum string states on their conserved charges and the stringtension proportional to lambda^(1/2). We consider states on the leading Reggetrajectory in the flat space limit which carry one or two (equal) spins inAdS_5 or S^5 and an orbital momentum in S^5, with Konishi multiplet statesbeing particular cases. We argue that the coefficients in the energy may befound by using a semiclassical expansion. By analyzing the examples of foldedspinning strings in AdS_5 and S^5 as well as three cases of circular two-spinstrings we demonstrate the universality of transcendental (zeta-function) partsof few leading coefficients. We also show the consistency with target spacesupersymmetry with different states belonging to the same multiplet having thesame non-trivial part of the energy. We suggest, in particular, that a rationalcoefficient (found by Basso for the folded string using Bethe Ansatzconsiderations and which, in general, is yet to be determined by a directtwo-loop string calculation) should, in fact, be universal.

"Short" spinning strings and structure of quantum AdS_5 x S^5 spectrum