Rodion Kuzmin
Rodion Kuzmin | |
---|---|
Rodion Kusmin, circa 1926 | |
Born |
Riabye village in the Haradok district | 9 October 1891
Died |
March 24, 1949 57) Leningrad | (aged
Nationality | Russian |
Fields | Mathematics |
Institutions | Perm State University, Tomsk Polytechnic University, Saint Petersburg State Polytechnical University |
Alma mater | Saint Petersburg State University nee Petrograd University |
Doctoral advisor | James Victor Uspensky |
Known for | Gauss–Kuzmin distribution, number theory and mathematical analysis. |
Rodion Osievich Kuzmin (Russian: Родион Осиевич Кузьмин, Nov. 9, 1891, Riabye village in the Haradok district – March 24, 1949, Leningrad) was a Russian mathematician, known for his works in number theory and analysis.[1] His name is sometimes transliterated as Kusmin.
Selected results
- In 1928, Kuzmin solved[2] 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[3] 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
Notes
- ↑ Venkov, B. A.; Natanson, I. P. "R. O. Kuz’min (1891–1949) (obituary)". Uspekhi Matematicheskikh Nauk. 4 (4): 148–155.
- ↑ Kuzmin, R.O. (1928). "On a problem of Gauss". DAN SSSR: 375–380.
- ↑ Kuzmin, R. O. (1930). "On a new class of transcendental numbers". Izvestiya Akademii Nauk SSSR (math.). 7: 585–597.
External links
- Rodion Kuzmin at the Mathematics Genealogy Project (The chronology there is apparently wrong, since J. V. Uspensky lived in USA from 1929.)
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