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A Khinchin Sequence
Author(s):
Thomas
Wieting
Journal:
Proc. Amer. Math. Soc.
136
(2008),
815-824.
MSC (2000):
Primary 11Y65;
Secondary 28D05
Posted:
November 30, 2007
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Abstract:
We prove that the geometric and harmonic means of the sequence  of positive integers proposed by Bailey, Borwein, and Crandall converge to the corresponding Khinchin Constants.
References:
-
- 1.
- D. H. Bailey, J. M. Borwein, R. C. Crandall, On the Khinchin Constant, Math. Comp. 66 (1997), 417-431. MR 1377659 (97c:11119)
- 2.
- J. G. van der Corput, Verteilungsfunktionen, Proc. Ned. Akad. v. Wet. 38 (1935), 813-821.
- 3.
- D. H. Lehmer, Note on an Absolute Constant of Khinchin, Amer. Math. Monthly, 46 (1939), 148-152. MR 1524526
- 4.
- C. Ryll-Nardzewski, On the Ergodic Theorems (I, II), Studia Math. 12 (1951), 65-79. MR 0046582 (13:757a); MR 0046583 (13:757b)
- 5.
- P. Walters, An Introduction to Ergodic Theory, Springer-Verlag, New York, 1982. MR 648108 (84e:28017)
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Additional Information:
Thomas
Wieting
Affiliation:
Department of Mathematics, Reed College, Portland, Oregon 97202
Email:
wieting@reed.edu
DOI:
10.1090/S0002-9939-07-09202-7
PII:
S 0002-9939(07)09202-7
Keywords:
Khinchin Sequence,
continued fraction expansion,
geometric mean,
harmonic mean
Received by editor(s):
January 12, 2007
Posted:
November 30, 2007
Additional Notes:
Thanks to R. C. Crandall for suggesting the subject of this paper.
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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