Rodion Kuzmin - Alchetron, The Free Social Encyclopedia

Nationality Russian Doctoral advisor J. V. Uspensky Fields Mathematics		Role Mathematician Name Rodion Kuzmin

Born 9 October 1891Riabye village in the Haradok district ( 1891-10-09 ) Institutions Perm State University, Tomsk Polytechnic University, Saint Petersburg State Polytechnical University Alma mater Saint Petersburg State University nee Petrograd University Known for Gauss–Kuzmin distribution, number theory and mathematical analysis. Died April 23, 1949, Saint Petersburg, Russia Institution Perm State University, Tomsk Polytechnic University, Peter the Great St. Petersburg Polytechnic University

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.

Selected results

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 forwhereGauss showed that Δ_n tends to zero as n goes to infinity, however, he was unable to give an explicit bound. Kuzmin showed that | Δ n ( s ) | ≤ C e − α n , 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 a^b, 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 f is continuously differentiable with monotonic derivative f ′ satisfying ∥ f ′ ( x ) ∥ ≥ λ > 0 (where ∥ ⋅ ∥ denotes the Nearest integer function) on a finite interval I , then

References

Rodion Kuzmin Wikipedia

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