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{{Infobox scientist
| name = Rodion Kuzmin
| image =Kusmin.jpg
| image_size = 120px
| caption = Rodion Kusmin, circa 1926
| birth_date =  {{birth date|1891|10|09|df=y}}
| birth_place = Riabye village in the [[Haradok]] district
| death_date =  {{death date and age|1949|04|23|1891|10|09}}
| death_place = [[Leningrad]]
| nationality = [[Russians|Russian]]
| field = [[Mathematics]]
| work_institution = [[Perm State University]], [[Tomsk Polytechnic University]], [[Saint Petersburg State Polytechnical University]]
| alma_mater = [[Saint Petersburg State University]] nee Petrograd University
| doctoral_advisor = [[J. V. Uspensky|James Victor Uspensky]]
| known_for =  [[Gauss–Kuzmin distribution]], [[number theory]] and [[mathematical analysis]].
}}
'''Rodion Osievich Kuzmin''' ({{lang-ru|Родион Осиевич Кузьмин}}, Nov. 9, 1891, Riabye village in the [[Haradok]] district &ndash; March 23, 1949, [[Leningrad]]) was a [[Russia]]n [[mathematician]], known for his works in [[number theory]] and [[mathematical analysis|analysis]].<ref>{{cite journal|last=Venkov|first=B. A.|last2=Natanson|first2=I. P.|author2-link=Isidor Natanson|title=R. O. Kuz’min (1891–1949) (obituary)|journal=Uspekhi matematicheskikh nauk|volume=4|issue=4|pages=148&ndash;155|url=http://mi.mathnet.ru/umn8643}}</ref>
 
==Selected results==
* In 1928, Kuzmin solved<ref>{{cite journal|last=Kuzmin|first=R.O.|title=On a problem of Gauss|journal=DAN SSSR|year=1928|pages=375&ndash;380}}</ref> the following problem due to [[Carl Friedrich Gauss|Gauss]] (see [[Gauss&ndash;Kuzmin distribution]]): if ''x'' is a random number chosen uniformly in (0,&nbsp;1), and
::<math> x = \frac{1}{k_1 + \frac{1}{k_2 + \cdots}}</math>
:is its [[continued fraction]] expansion, find a bound for
::<math> \Delta_n(s) = \mathbb{P} \left\{ x_n \leq s \right\} - \log_2(1+s),</math>
:where
::<math> x_n = \frac{1}{k_{n+1} + \frac{1}{k_{n+2} + \cdots}} .</math>
:Gauss showed that ''&Delta;''<sub>''n''</sub> tends to zero as ''n'' goes to infinity, however, he was unable to give an explicit bound. Kuzmin showed that
::<math>  |\Delta_n(s)| \leq  C e^{- \alpha \sqrt{n}}~,</math>
:where ''C'',''&alpha;''&nbsp;>&nbsp;0 are numerical constants. In 1929, the bound was improved to ''C''&nbsp;0.7<sup>''n''</sup> by [[Paul Lévy (mathematician)|Paul Lévy]].
 
* In 1930, Kuzmin proved<ref>{{cite journal|last=Kuzmin|first=R. O.|title=On a new class of transcendental numbers|journal=Izvestiya Akademii Nauk SSSR (math.)|volume=7|year=1930|pages=585&ndash;597|url=http://mi.mathnet.ru/eng/izv5316}}</ref> that numbers of the form ''a''<sup>''b''</sup>, where ''a'' is [[algebraic number|algebraic]] and ''b'' is a real [[quadratic irrational]], are [[transcendental number|transcendental]]. In particular, this result implies that [[Gelfond–Schneider constant]]
::<math>2^{\sqrt{2}}=2.6651441426902251886502972498731\ldots</math>
:is transcendental. See [[Gelfond–Schneider theorem]] for later developments.
 
==Notes==
{{Reflist}}
 
==External links==
* {{MathGenealogy|id=152494}} (The chronology there is apparently wrong, since [[J. V. Uspensky]] lived in USA from 1929.)
 
{{Persondata
| NAME              = Kuzmin, Rodion
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = Russian mathematician
| DATE OF BIRTH    = October 9, 1891
| PLACE OF BIRTH    = Riabye village in the [[Haradok]] district
| DATE OF DEATH    = April 23, 1949
| PLACE OF DEATH    = [[Leningrad]]
}}
{{DEFAULTSORT:Kuzmin, Rodion}}
[[Category:1891 births]]
[[Category:1949 deaths]]
[[Category:People from Vitebsk Governorate]]
[[Category:Soviet mathematicians]]
[[Category:Russian mathematicians]]
[[Category:Perm State University faculty]]
[[Category:Number theorists]]
[[Category:Mathematical analysts]]

Revision as of 21:04, 11 January 2014

Template:Infobox scientist Rodion Osievich Kuzmin (My name is Jordan (41 years old) and my hobbies are Microscopy and Canoeing.

Check out my weblog Hostgator Review, Nov. 9, 1891, Riabye village in the Haradok district – March 23, 1949, Leningrad) was a Russian mathematician, known for his works in number theory and analysis.[1]

Selected results

x=1k1+1k2+
is its continued fraction expansion, find a bound for
Δn(s)={xns}log2(1+s),
where
xn=1kn+1+1kn+2+.
Gauss showed that Δn tends to zero as n goes to infinity, however, he was unable to give an explicit bound. Kuzmin showed that
|Δn(s)|Ceαn,
where C,α > 0 are numerical constants. In 1929, the bound was improved to C 0.7n by Paul Lévy.
22=2.6651441426902251886502972498731
is transcendental. See Gelfond–Schneider theorem for later developments.

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

  • 50 yr old Print Journalist Broadbent from Deep River, has hobbies and interests which includes r/c helicopters, property developers in singapore house for rent and scrabble. Suggests that you go to Tomb of Askia. (The chronology there is apparently wrong, since J. V. Uspensky lived in USA from 1929.)

Template:Persondata

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