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 Mikhail Alekseevich Lavrent'ev (photo) For the 50th birthday of Mikhail Alekseevich Lavrent'evM. V. Keldysh 3 On quasi-polynomials deviating least from zero on the segment $[0,1]$A. O. Gel'fond 9 Normal periodic systems and their applications to the estimation of sums of fractional partsN. M. Korobov 17 On the laws of distribution of the fractional parts of an exponential functionI. I. Shapiro-Pyatetskii 47 The approximation of certain transcendental numbers. I. Approximation of logarithms of algebraic numbersN. I. Fel'dman 53 Bilinear integrals of linear hyperbolic problemsD. M. Volkov 75 On the zeros of Riemann's zeta-functionV. T. Mironov 91 On continuous images of Hilbert spaceR. Yu. Matskina 95