Naum Ilyich Feldman

Naum Ilyich Feldman , Russian Наум Ильич Фельдман (born November 26, 1918 in Melitopol , † April 20, 1994 in Moscow ) was a Soviet mathematician who dealt with number theory .

life and work

Feldman studied mathematics from 1936 at the University of Leningrad with a focus on number theory with Rodion Kusmin . After graduating in 1941, he was a soldier in the Red Army, fought in the defense of Moscow and the conquest of Koenigsberg, and received several awards. From 1946 he continued his studies in Moscow and received his doctorate in 1949 under Alexander Gelfond . From 1950 to 1954 he headed the mathematics department at the Ufimsky Oil Institute and lectured at the Moscow Institute for Geophysical Prospecting from 1954 to 1961. From 1961 he was at Lomonosov University , completed his habilitation in 1974 (Russian doctorate) and was given a full professorship in 1980.

He dealt with Diophantine approximation , transcendent numbers and Diophantine equations . He improved Gelfond's method for proving Gelfond-Schneider's theorem for estimates of transcendence (measures of transcendence according to Émile Borel ) of logarithms of algebraic numbers . This happened in his dissertation, later he extended this to periods of elliptic curves and the number of circles . ${\ displaystyle \ pi}$

He also tightened a theorem by Liouville (see Diophantine approximation ) about the approximation of algebraic numbers by rational numbers, in which he gave effective values for the constants: If an algebraic number of degree , then there are effective positive constants , with ${\ displaystyle \ alpha}$ ${\ displaystyle n> 3}$ ${\ displaystyle a}$ ${\ displaystyle C}$

{\ displaystyle \ left | \ alpha - {\ frac {p} {q}} \ right |> C \, q ^ {(an)}}

for all integers with . ${\ displaystyle p, q}$ ${\ displaystyle q> 0}$

Fonts

The measure of transcendency of the number ${\ displaystyle \ pi}$ , Izv. Akad. Nauk SSSR Ser. Mat., Volume 24, 1960, Issue 3, pp. 357-368 (Russian), English translation American Math. Soc. Translations (2), vol. 58, 1966, pp. 110-124.
Approximation by algebraic numbers to logarithms of algebraic numbers , Izv. Akad. Nauk SSSR Ser. Mat., Vol. 24, 1960, pp. 475-492 (Russian), English translation American Math. Soc. Translations (2), Vol. 58, 1966, pp. 125-142
with Andrei Borissowitsch Schidlowski : The Development And Present State Of The Theory Of Transcendental Numbers , Russian Mathematical Surveys, Volume 22, 1967, pp. 1-79.
Improved Estimate For A Linear Form Of The Logarithms Of Algebraic Numbers, Mathematics of the USSR-Sbornik, Volume 6, 1968, pp. 393-406
Approximation of number π by algebraic numbers from special fields , J. Number Theory, Volume 9, 1977, pp. 48-60.
Effective bounds for the number of solutions of certain diophantine equations , Mathematical Notes of the Academy of Sciences of the USSR, Volume 8, 1970, pp. 674-679.
Hilbert`s seventh problem , Moscow, Lomonossow University 1982
with Juri Walentinowitsch Nesterenko : Number Theory IV: Transcendental numbers , (Encyclopaedia of Mathematical Sciences 44), Springer 1997, ISBN 978-3540614678
Algebraic and transcental numbers, Quantum 2000, pdf

literature

NM Korobov, Yu. V. Nesterenko, AB Shidlovskii: Naum Il'ich Feld'man (obituary) , Russian Mathematical Surveys, Volume 50, 1995, pp. 1247-1252.

Web links

John J. O'Connor, Edmund F. Robertson : Naum Iljitsch Feldman. In: MacTutor History of Mathematics archive .
Entry at mathnet.ru

Individual evidence

^ Feldman, An effective power sharpening of a theorem of Liouville, Izv. Akad. Nauk SSSR Ser. Mat., Vol. 35, 1971, pp. 973-990

personal data
SURNAME	Feldman, Naum Ilyich
BRIEF DESCRIPTION	Russian mathematician
DATE OF BIRTH	November 26, 1918
PLACE OF BIRTH	Melitopol
DATE OF DEATH	April 20, 1994
Place of death	Moscow

[1] Feldman, An effective power sharpening of a theorem of Liouville, Izv. Akad. Nauk SSSR Ser. Mat., Vol. 35, 1971, pp. 973-990