31:
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324:
1119:
150:
434:
681:
545:
244:
889:
211:
1099:
781:
95:
1114:
1104:
670:
1069:
721:
228:
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Atti del
Congresso Internazionale dei Matematici: Bologna del 3 al 10 de settembre di 1928
8:
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540:
goes to infinity, however, he was unable to give an explicit bound. Kuzmin showed that
316:
418:{\displaystyle \Delta _{n}(s)=\mathbb {P} \left\{x_{n}\leq s\right\}-\log _{2}(1+s),}
210:. His name is sometimes transliterated as Kusmin. He was an Invited Speaker of the
654:
183:
157:
986:
1073:
162:
632: > 0 are numerical constants. In 1929, the bound was improved to
1083:
1065:
203:
199:
110:
132:
516:{\displaystyle x_{n}={\frac {1}{k_{n+1}+{\frac {1}{k_{n+2}+\cdots }}}}.}
709:{\displaystyle 2^{\sqrt {2}}=2.6651441426902251886502972498731\ldots }
195:
74:
1040:
85:
191:
55:
989:
613:{\displaystyle |\Delta _{n}(s)|\leq Ce^{-\alpha {\sqrt {n}}}~,}
304:{\displaystyle x={\frac {1}{k_{1}+{\frac {1}{k_{2}+\cdots }}}}}
959:{\displaystyle \sum _{n\in I}e^{2\pi if(n)}\ll \lambda ^{-1}.}
753:
is continuously differentiable with monotonic derivative
30:
235:
is a random number chosen uniformly in (0, 1), and
892:
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784:
759:
739:
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548:
437:
327:
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223:
In 1928, Kuzmin solved the following problem due to
823:{\displaystyle \Vert f'(x)\Vert \geq \lambda >0}
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708:
612:
515:
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1072:(The chronology there is apparently wrong, since
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645:In 1930, Kuzmin proved that numbers of the form
151:Saint Petersburg State Polytechnical University
1024:Kuzmin, R.O. (1928). "On a problem of Gauss".
843:
837:
805:
785:
1041:"On a new class of transcendental numbers"
1010:Kuzmin, R. "Sur un problĆØme de Gauss." In
984:
669:. In particular, this result implies that
351:
190:, 9 November 1891, Riabye village in the
1120:Academic staff of Perm State University
1082:
1038:
1023:
990:"R. O. Kuz'min (1891ā1949) (obituary)"
1045:Izvestiya Akademii Nauk SSSR (Math.)
217:
13:
849:{\displaystyle \Vert \cdot \Vert }
555:
329:
14:
1131:
1059:
701:2.6651441426902251886502972498731
96:Saint Petersburg State University
194:district – 24 March 1949,
29:
229:Gauss–Kuzmin distribution
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1:
1070:Mathematics Genealogy Project
994:Uspekhi Matematicheskikh Nauk
1100:People from Gorodoksky Uyezd
319:expansion, find a bound for
147:Tomsk Polytechnic University
7:
10:
1136:
1014:, vol. 6, pp. 83ā90. 1929.
671:GelfondāSchneider constant
729:He is also known for the
722:GelfondāSchneider theorem
202:, known for his works in
187:
168:
156:
138:
128:
121:
107:GaussāKuzmin distribution
102:
91:
81:
63:
40:
35:Rodion Kusmin, circa 1926
28:
21:
1076:lived in USA from 1929.)
971:
858:Nearest integer function
731:Kusmin-Landau inequality
98:nee Petrograd University
860:) on a finite interval
724:for later developments.
720:is transcendental. See
1039:Kuzmin, R. O. (1930).
960:
874:
850:
824:
772:
747:
710:
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517:
419:
305:
188:Š Š¾Š“ŠøŠ¾Š½ ŠŃŠøŠµŠ²ŠøŃ ŠŃŠ·ŃŠ¼ŠøŠ½
175:Rodion Osievich Kuzmin
54:Riabye village in the
1115:Mathematical analysts
1105:Soviet mathematicians
1026:Dokl. Akad. Nauk SSSR
961:
875:
851:
825:
773:
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163:James Victor Uspensky
143:Perm State University
115:mathematical analysis
16:Russian mathematician
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663:quadratic irrational
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214:in 1928 in Bologna.
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771:{\displaystyle f'}
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527:Gauss showed that
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317:continued fraction
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873:{\displaystyle I}
746:{\displaystyle f}
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536:tends to zero as
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123:Scientific career
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51:9 October 1891
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1066:Rodion Kuzmin
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1000:(4): 148ā155.
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67:24 March 1949
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23:Rodion Kuzmin
20:
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856:denotes the
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528:
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174:
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139:Institutions
122:
69:(1949-03-24)
1095:1949 deaths
1090:1891 births
778:satisfying
133:Mathematics
82:Nationality
1084:Categories
1051:: 585ā597.
1028:: 375ā380.
661:is a real
47:1891-10-09
946:−
942:λ
938:≪
918:π
902:∈
895:∑
844:‖
841:⋅
838:‖
812:λ
809:≥
806:‖
786:‖
704:…
655:algebraic
638:Paul LĆ©vy
593:α
590:−
579:≤
556:Δ
502:⋯
395:
382:−
371:≤
330:Δ
293:⋯
196:Leningrad
180:ā¹See Tfdāŗ
75:Leningrad
793:′
765:′
649:, where
208:analysis
58:district
1068:at the
830:(where
315:is its
192:Haradok
184:Russian
86:Russian
56:Haradok
880:, then
665:, are
630:α
624:where
605:
529:Δ
429:where
231:): if
129:Fields
972:Notes
733:: If
227:(see
225:Gauss
815:>
657:and
206:and
113:and
64:Died
41:Born
653:is
386:log
212:ICM
1086::
1047:.
1043:.
996:.
992:.
186::
149:,
145:,
109:,
1049:7
998:4
954:.
949:1
933:)
930:n
927:(
924:f
921:i
915:2
911:e
905:I
899:n
868:I
818:0
803:)
800:x
797:(
790:f
762:f
741:f
698:=
692:2
687:2
659:b
651:a
647:a
640:.
634:C
628:,
626:C
608:,
598:n
586:e
582:C
575:|
571:)
568:s
565:(
560:n
551:|
538:n
533:n
511:.
499:+
494:2
491:+
488:n
484:k
479:1
474:+
469:1
466:+
463:n
459:k
454:1
449:=
444:n
440:x
413:,
410:)
407:s
404:+
401:1
398:(
390:2
378:}
374:s
366:n
362:x
357:{
352:P
348:=
345:)
342:s
339:(
334:n
290:+
285:2
281:k
276:1
271:+
266:1
262:k
257:1
252:=
249:x
233:x
177:(
117:.
49:)
45:(
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