Rodion Kuzmin
Russian mathematician
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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]
Born9 October 1891
Riabye village in the Haradok district
Died24 March 1949 (aged 57)
AlmamaterSaint Petersburg State University nee Petrograd University
KnownforGauss–Kuzmin distribution, number theory and mathematical analysis.
Rodion Kuzmin | |
|---|---|
Rodion Kusmin, circa 1926 | |
| Born | 9 October 1891 Riabye village in the Haradok district |
| Died | 24 March 1949 (aged 57) |
| Alma mater | Saint Petersburg State University nee Petrograd University |
| Known for | Gauss–Kuzmin distribution, number theory and mathematical analysis. |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Perm State University, Tomsk Polytechnic University, Saint Petersburg State Polytechnical University |
| Doctoral advisor | James Victor Uspensky |
Selected results
- In 1928, Kuzmin solved[3] the following problem due to Gauss (see Gauss–Kuzmin distribution): if x is a random number chosen uniformly in (0, 1), and
- 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.
- In 1930, Kuzmin proved[4] that numbers of the form ab, where a is algebraic and b is a real quadratic irrational, are transcendental. In particular, this result implies that Gelfond–Schneider constant
- 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
