31:
418:
516:
709:
613:
304:
959:
823:
849:
725:
771:
873:
746:
319:
1114:
150:
429:
676:
540:
239:
884:
206:
1094:
776:
95:
1109:
1099:
665:
1064:
716:
223:
106:
146:
632:
828:
1104:
852:
661:
202:
142:
114:
1089:
1084:
657:
219:
1007:
Atti del
Congresso Internazionale dei Matematici: Bologna del 3 al 10 de settembre di 1928
8:
751:
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731:
535:
goes to infinity, however, he was unable to give an explicit bound. Kuzmin showed that
311:
413:{\displaystyle \Delta _{n}(s)=\mathbb {P} \left\{x_{n}\leq s\right\}-\log _{2}(1+s),}
205:. His name is sometimes transliterated as Kusmin. He was an Invited Speaker of the
649:
178:
157:
981:
1068:
162:
627: > 0 are numerical constants. In 1929, the bound was improved to
1078:
1060:
198:
194:
110:
132:
511:{\displaystyle x_{n}={\frac {1}{k_{n+1}+{\frac {1}{k_{n+2}+\cdots }}}}.}
704:{\displaystyle 2^{\sqrt {2}}=2.6651441426902251886502972498731\ldots }
190:
74:
1035:
85:
186:
55:
984:
608:{\displaystyle |\Delta _{n}(s)|\leq Ce^{-\alpha {\sqrt {n}}}~,}
299:{\displaystyle x={\frac {1}{k_{1}+{\frac {1}{k_{2}+\cdots }}}}}
954:{\displaystyle \sum _{n\in I}e^{2\pi if(n)}\ll \lambda ^{-1}.}
748:
is continuously differentiable with monotonic derivative
30:
230:
is a random number chosen uniformly in (0, 1), and
887:
861:
831:
779:
754:
734:
679:
543:
432:
322:
242:
218:
In 1928, Kuzmin solved the following problem due to
818:{\displaystyle \Vert f'(x)\Vert \geq \lambda >0}
953:
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843:
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765:
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703:
607:
510:
412:
298:
1067:(The chronology there is apparently wrong, since
1076:
640:In 1930, Kuzmin proved that numbers of the form
151:Saint Petersburg State Polytechnical University
1019:Kuzmin, R.O. (1928). "On a problem of Gauss".
838:
832:
800:
780:
1036:"On a new class of transcendental numbers"
1005:Kuzmin, R. "Sur un problĆØme de Gauss." In
979:
664:. In particular, this result implies that
346:
185:, 9 November 1891, Riabye village in the
1115:Academic staff of Perm State University
1077:
1033:
1018:
985:"R. O. Kuz'min (1891ā1949) (obituary)"
1040:Izvestiya Akademii Nauk SSSR (Math.)
212:
13:
844:{\displaystyle \Vert \cdot \Vert }
550:
324:
14:
1126:
1054:
696:2.6651441426902251886502972498731
96:Saint Petersburg State University
189:district – 24 March 1949,
29:
224:Gauss–Kuzmin distribution
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1012:
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973:
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921:
797:
791:
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565:
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404:
392:
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1:
1065:Mathematics Genealogy Project
989:Uspekhi Matematicheskikh Nauk
1095:People from Gorodoksky Uyezd
314:expansion, find a bound for
147:Tomsk Polytechnic University
7:
10:
1131:
1009:, vol. 6, pp. 83ā90. 1929.
666:GelfondāSchneider constant
724:He is also known for the
717:GelfondāSchneider theorem
197:, known for his works in
182:
168:
156:
138:
128:
121:
107:GaussāKuzmin distribution
102:
91:
81:
63:
40:
35:Rodion Kusmin, circa 1926
28:
21:
1071:lived in USA from 1929.)
966:
853:Nearest integer function
726:Kusmin-Landau inequality
98:nee Petrograd University
855:) on a finite interval
719:for later developments.
715:is transcendental. See
1034:Kuzmin, R. O. (1930).
955:
869:
845:
819:
767:
742:
705:
609:
512:
414:
300:
183:Š Š¾Š“ŠøŠ¾Š½ ŠŃŠøŠµŠ²ŠøŃ ŠŃŠ·ŃŠ¼ŠøŠ½
175:Rodion Osievich Kuzmin
54:Riabye village in the
1110:Mathematical analysts
1100:Soviet mathematicians
1021:Dokl. Akad. Nauk SSSR
956:
870:
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163:James Victor Uspensky
143:Perm State University
115:mathematical analysis
16:Russian mathematician
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658:quadratic irrational
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209:in 1928 in Bologna.
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766:{\displaystyle f'}
763:
738:
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522:Gauss showed that
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312:continued fraction
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868:{\displaystyle I}
741:{\displaystyle f}
689:
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595:
531:tends to zero as
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123:Scientific career
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1105:Number theorists
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92:Alma mater
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1055:External links
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71:(aged 57)
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51:9 October 1891
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1061:Rodion Kuzmin
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995:(4): 148ā155.
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67:24 March 1949
66:
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23:Rodion Kuzmin
20:
1043:
1039:
1029:
1020:
1014:
1006:
1001:
992:
988:
975:
851:denotes the
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523:
227:
174:
173:
139:Institutions
122:
69:(1949-03-24)
1090:1949 deaths
1085:1891 births
773:satisfying
133:Mathematics
82:Nationality
1079:Categories
1046:: 585ā597.
1023:: 375ā380.
656:is a real
47:1891-10-09
941:−
937:λ
933:≪
913:π
897:∈
890:∑
839:‖
836:⋅
833:‖
807:λ
804:≥
801:‖
781:‖
699:…
650:algebraic
633:Paul LĆ©vy
588:α
585:−
574:≤
551:Δ
497:⋯
390:
377:−
366:≤
325:Δ
288:⋯
191:Leningrad
75:Leningrad
788:′
760:′
644:, where
203:analysis
58:district
1063:at the
825:(where
310:is its
187:Haradok
179:Russian
86:Russian
56:Haradok
875:, then
660:, are
625:α
619:where
600:
524:Δ
424:where
226:): if
129:Fields
967:Notes
728:: If
222:(see
220:Gauss
810:>
652:and
201:and
113:and
64:Died
41:Born
648:is
381:log
207:ICM
1081::
1042:.
1038:.
991:.
987:.
181::
149:,
145:,
109:,
1044:7
993:4
949:.
944:1
928:)
925:n
922:(
919:f
916:i
910:2
906:e
900:I
894:n
863:I
813:0
798:)
795:x
792:(
785:f
757:f
736:f
693:=
687:2
682:2
654:b
646:a
642:a
635:.
629:C
623:,
621:C
603:,
593:n
581:e
577:C
570:|
566:)
563:s
560:(
555:n
546:|
533:n
528:n
506:.
494:+
489:2
486:+
483:n
479:k
474:1
469:+
464:1
461:+
458:n
454:k
449:1
444:=
439:n
435:x
408:,
405:)
402:s
399:+
396:1
393:(
385:2
373:}
369:s
361:n
357:x
352:{
347:P
343:=
340:)
337:s
334:(
329:n
285:+
280:2
276:k
271:1
266:+
261:1
257:k
252:1
247:=
244:x
228:x
177:(
117:.
49:)
45:(
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