Aleksandr Osipovich Gelfond
Born: 24 Oct 1906 in St Petersburg, Russia
Died: 7 Nov 1968 in Moscow, Russia
Previous (Chronologically) Next Biographies Index Previous ( Alphabetically) Next Welcome page
Previous (Chronologically) Next Biographies Index Previous ( Alphabetically) Next Welcome page
Gelfond developed basic techniques in the study of transcendental numbers.
Gelfond taught mathematics at the Moscow Technological College (1929-30) and then from 1931 at Moscow State University where he held chairs of analysis, theory of numbers and the history of mathematics.
In addition to his important work in the number theory of transcendental numbers (that is, numbers that are not the solution of an algebraic equation with rational coefficients) Gelfond made significant contributions to the theory of interpolation and the approximation of functions of a complex variable.
In 1929 he conjectured that:-
If a
, 1 
n m, b,1 n m are algebraic numbers such that {ln a, 1 n m} are linearly independent over Q, then
b
ln a + b
ln a + ... + b
ln a 
0.
In 1934 Gelfond proved a special case of his conjecture namely that aġ is transcendental if a is algebraic (a 0,1) and b is an irrational algebraic number. This result is now known as Gelfond's theorem and solved Problem 23 of the list of Hilbert problems. It was solved independently by Schneider.
In 1966 A Baker proved Gelfond's Conjecture in general.
Gelfond's major contributions to transcendental numbers are in Transtendentnye i algebraicheskie chisla (1952) and to approximation and interpolation theories are in Ischislenie konechnykh raznostey (1952).
References:
Previous (Chronologically) Next Biographies Index Previous ( Alphabetically) Next Welcome page History Topics Index Famous curves index Chronologies Birthplace Map Mathematicians of the day Anniversaries for the year Search Form Simple Search Form Search Suggestions