Rodion Kuzmin

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Rodion Kuzmin
Kusmin.jpg
Rodion Kusmin, circa 1926
Born (1891-10-09)9 October 1891
Riabye village in the Haradok district
Died March 24, 1949(1949-03-24) (aged 57)
Leningrad
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[edit]

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[edit]

  1. ^ Venkov, B. A.; Natanson, I. P. "R. O. Kuz’min (1891–1949) (obituary)". Uspekhi Matematicheskikh Nauk 4 (4): 148–155. 
  2. ^ Kuzmin, R.O. (1928). "On a problem of Gauss". DAN SSSR: 375–380. 
  3. ^ Kuzmin, R. O. (1930). "On a new class of transcendental numbers". Izvestiya Akademii Nauk SSSR (math.) 7: 585–597. 

External links[edit]