Vyacheslav Alekseevich Oleinikov (obituary)

On the night of 4 — 5 March 1989 Vyacheslav Alekseevich Oleinikov, professor of the theory of functions and functional analysis in the faculty of mechanics and mathematics of Moscow State University, died tragically in a fire at his house outside Moscow. Oleinikov was born on 10 March 1939 in Moscow. In 1956 he enrolled in the faculty of mechanics and mathematics of Moscow State University. After graduating (in 1961) he worked for two years in the Computer Laboratory at Moscow State University (and later on he kept up his interest in applied problems: he published several papers on work connected with economic treaties). In 1963 he became a research student in the faculty of mechanics and mathematics of Moscow State University in the department of number theory (of which A.O. Gel'fond was then the director) and his supervisor was A.B. Shidlovskii. Oleinikov's main research interests were problems of transcendental numbers, which are closely linked to algebraic and classical transcendental functions and differential equations. In 1929 C.L. Siegel propounded a method (based on the ideas of Hermite and Lindemann) which made it possible to study the arithmetical nature of the values at algebraic points of quite a wide class of entire analytic functions (Siegel's ^-functions), which satisfy linear differential equations with polynomial coefficients. In 1955 Shidlovskii developed Siegel's ideas and completely reduced the arithmetical problem of the transcendental nature and algebraic independence of the values of such functions at algebraic points to the function-theoretic independence of these same functions (and their derivatives) over the field of rational functions. However in real situations the application of Shidlovskii's theorem ran into significant difficulties; in particular, it was not possible to investigate fully the question of the independence of y(oc), /(a), / '(a) for the classical i?-function