Alexander Gelfond

Alexander Gelfond Ossipowitsch (Russian Александр Осипович Гельфонд; * 11.jul / October 24 1906greg in Saint Petersburg, .. † 7 November 1968, Moscow) was a Russian mathematician.

Biography

Gelfond was born on 24 October 1906 as the son of a doctor. He studied from 1924 to 1927 at the University of Moscow and continued his postgraduate training at Alexander Khinchin ( 1894-1959 ) and Vyacheslav Stepanov ( 1889-1950 ) continued. After a brief teaching career at the Technical University of Moscow he was in 1931 Professor of Analysis, later for number theory at Moscow University. He held until his death, from 1933 complemented by an activity at the Moscow Steklov Institute of Mathematics of this position. In 1935, he received a PhD in mathematics and physics.

Gelfond achieved especially in the field of number theory excellent results. He built the traditions of the Russian Soviet mathematics in this field and was a co-founder of a successful Soviet school of number theory. In 1929 he discovered deep connections between the growth and other properties of entire analytic functions and the arithmetic of their values ​​and thus solved the seventh Hilbert problem for a special case. After improving his method, among others, the consideration of linear forms of exponentials, he succeeded in 1934 to prove that for an algebraic number a ≠ 0 or 1, and an algebraic irrational number b, the number is transcendental ( set of Gelfond -Schneider). Regardless of the Hilbert's seventh problem was only a little later solved by Theodor Schneider ( 1911-1988 ). An obvious generalization of the theorem was proved in 1966 by Alan Baker. Gelfonds results and the application of his methods led to significant advances in the theory of transcendental numbers. He constructed new classes of transcendental numbers, sparked questions about the mutual independence of algebraic numbers and extended the method successfully on p- adic functions. In 1952, he took many results together in a monograph " Transzendentnyje i algebraitscheskije Čisla " ( Трансцендентные и алгебраические числа ).

A conjecture of Gelfond, which remains unresolved, expanding the set of Gelfond - Schneider systems of numbers () and suggested that these are mutually algebraically independent over the rational numbers, if the algebraic numbers, linearly independent over the rational numbers are. The best result came in 1989 G. Diaz, who showed that the transcendence degree of the system of numbers ( with a irrational ) is least. Gelfond proved itself a special case (n = 2, a cubic irrational number ).

Partial closely related to the number-theoretic studies were Gelfonds research for interpolation and approximation of functions of a complex variable. Incoming he examined the convergence of interpolation depending on the amount of points given and the properties of the function to be approximated, and the unique determination of the constructed function. He put these results in 1952 in the monograph together as " calculus of finite differences " appeared in 1958 in German translation. Other topics included the completeness of functional systems and the asymptotic behavior of the eigenvalues ​​of certain integral equations.

In addition, the history of mathematics Gelfonds found interest, he promoted it, especially with studies on the number-theoretic Euler's work.