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We present structural improvements of Esseen's (1969) and Rozovskii's (1974)estimates for the rate of convergence in the Lindeberg theorem and also computethe appearing absolute constants. We introduce the asymptotically exactconstants in the constructed inequalities and obtain upper bounds for them. Weanalyze the values of Esseen's, Rozovskii's, and Lyapunov's fractions, comparethem pairwise and provide some extremal distributions. As an auxiliarystatement, we prove a sharp inequality for the quadratic tails of an arbitrarydistribution (with finite second order moment) and its convolutionalsymmetrization.

Esseen-Rozovskii type estimates for the rate of convergence in the Lindeberg theorem