Rodion Kusmin, circa 1926
|Born||9 October 1891|
Riabye village in the Haradok district
|Died||March 24, 1949 (aged 57)|
|Alma mater||Saint Petersburg State University nee Petrograd University|
|Known for||Gauss–Kuzmin distribution, number theory and mathematical analysis.|
|Institutions||Perm State University, Tomsk Polytechnic University, Saint Petersburg State Polytechnical University|
|Doctoral advisor||James Victor Uspensky|
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. His name is sometimes transliterated as Kusmin. He was an Invited Speaker of the ICM in 1928 in Bologna.
- In 1928, Kuzmin solved 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
- 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 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
- Venkov, B. A.; Natanson, I. P. "R. O. Kuz'min (1891–1949) (obituary)". Uspekhi Matematicheskikh Nauk. 4 (4): 148&ndash, 155.
- Kuzmin, R. "Sur un problème de Gauss." In Atti del Congresso Internazionale dei Matematici: Bologna del 3 al 10 de settembre di 1928, vol. 6, pp. 83–90. 1929.
- Kuzmin, R.O. (1928). "On a problem of Gauss". Dokl. Akad. Nauk SSSR: 375&ndash, 380.
- Kuzmin, R. O. (1930). "On a new class of transcendental numbers". Izvestiya Akademii Nauk SSSR (math.). 7: 585&ndash, 597.