Aleksandr Gelfond

Aleksandr Osipovich Gelfond (October 24th 1906, Saint-Pétersbourg - November 7th 1968, Moscow) was a Russian Mathématicien , author of the Théorème of Gelfond.

Biography

Aleksandr Gelfond was born with Petrograd (currently Saint-Pétersbourg) in a family whose father, Osip Isaakovich Gelfond, were Physicien and Philosophe amateur. It integrates the Université of Moscow in 1924 and obtains its diploma of Doctor of philosophy in 1930. Its work was framed by Aleksandr Khinchin and Vyacheslav Stepanov.

In 1930 it worked for 5 months in Germany (with Berlin and Göttingen) where it collaborated with Edmund Landau, Carl Ludwig Siegel and David Hilbert. In 1931, it started to teach, as a professor with the Université of Moscow, where it worked until the end of his life. Since 1933, it worked in parallel with the Institut of mathematics Steklov. In 1939, he was elected member of the Academy of Science of the USSR.

Work

Alexandr Gelfond obtained important results in several mathematical fields, in particular in the Théorie of the numbers, Théorie of the analytical functions, integral equations. Its result more célèbe is the Théorème of Gelfond:

If $\backslash \; alpha$ and $\backslash \; beta$ is algebraic numbers (with $\backslash \; alpha\; \backslash \; neq\; 0$ and $\backslash \; alpha\; \backslash \; neq\; 1$), and if $\backslash \; beta$ is not a real number rational, then the number $\backslash \; alpha^\; \{\backslash \; beta\}$ is a transcendent Nombre.

This statement is that of the famous 7^ième problem of Hilbert. Gelfond pouvé a particular case of the theorem in 1929, when he was studied graduate, and completely in 1934 showed it. In 1935, the theorem was shown independently by Theodor Schneider, with the result that this theorem is usually called Théorème of Gelfond-Schneider. In 1929 Gelfond proposed an extension of the theorem, known under the name of Conjecture of Gelfond, which was proven by Alan Baker in 1966.

Before work of Gelfond, few numbers were known to be transcendent. One knew then E and pi checking this property. After its work, the transcendence of an infinity of number could be easily shown. Some of them were named in the honor of Gelfond:

• $2^\; \{\backslash \; sqrt\; \{2\}\}$, known like the Constant of Gelfond-Schneider
• $e^\; \backslash \; pi\; \backslash ,$, known like the Constant of Gelfond