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 Sergei Ivanovich Vavilov 24.III.1891–25.I.1951 (photo) In memory of the great science worker and organizer Sergei Ivanovich Vavilov General theorems on the upper bound of the modulus of a trigonometric sumI. M. Vinogradov 109 Hilbert space and the theory of numbers. IIN. P. Romanov 131 The approximation of certain transcendental numbers. II. The approximation of certain numbers connected with the Weierstrass function $\wp(z)$N. I. Fel'dman 153 Right-alternative fieldsL. A. Skornyakov 177 The fundamental $n$-harmonic problem for multiply connected regionsA. I. Kalandiya 185