Russian mathematician
Rodion Osievich Kuzmin (Russian: Родион Осиевич Кузьмин, 9 November 1891, Riabye village in the Haradok district – 24 March 1949, Leningrad) was a Soviet mathematician, known for his works in number theory and analysis.[1] His name is sometimes transliterated as Kusmin. He was an Invited Speaker of the ICM in 1928 in Bologna.[2]
Selected results
- is its continued fraction expansion, find a bound for
- where
- Gauss showed that Δn tends to zero as n goes to infinity, however, he was unable to give an explicit bound. Kuzmin showed that
- where C,α > 0 are numerical constants. In 1929, the bound was improved to C 0.7n by Paul Lévy.
- is transcendental. See Gelfond–Schneider theorem for later developments.
- He is also known for the Kusmin-Landau inequality: If is continuously differentiable with monotonic derivative satisfying (where denotes the Nearest integer function) on a finite interval , then
Notes
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