A Gaussian measure for certain continued fractions
Author:
Sofia Kalpazidou
Journal:
Proc. Amer. Math. Soc. 96 (1986), 629635
MSC:
Primary 11K50; Secondary 28D99
MathSciNet review:
826493
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Abstract: We solve a variant of Gauss' problem for grotesque continued fraction using the approach of dependence with complete connections.
 [1]
Şerban
Grigorescu and Marius
Iosifescu, Dependenţă cu legături complete
şi aplicaţii, Editura Ştiinţifică
si Enciclopedicǎ, Bucharest, 1982 (Romanian). With an English
summary. MR
692365 (85d:60102)
 [2]
M.
Iosifescu and R.
Theodorescu, Random processes and learning, SpringerVerlag,
New York, 1969. Die Grundlehren der mathematischen Wissenschaften, Band
150. MR
0293704 (45 #2781)
 [3]
Mark
Kac, Statistical independence in probability, analysis and number
theory., The Carus Mathematical Monographs, No. 12, Published by the
Mathematical Association of America. Distributed by John Wiley and Sons,
Inc., New York, 1959. MR 0110114
(22 #996)
 [4]
Sofia
Kalpazidou, Some asymptotic results on digits of the nearest
integer continued fraction, J. Number Theory 22
(1986), no. 3, 271–279. MR 831872
(87i:11101), http://dx.doi.org/10.1016/0022314X(86)900119
 [5]
Sofia
Kalpazidou, On a random system with complete connections associated
with the continued fraction to the nearer integer expansion, Rev.
Roumaine Math. Pures Appl. 30 (1985), no. 7,
527–537. MR
826234 (87i:11100)
 [6]
M.
Frank Norman, Markov processes and learning models, Academic
Press, New YorkLondon, 1972. Mathematics in Science and Engineering, Vol.
84. MR
0423546 (54 #11522)
 [7]
G.
J. Rieger, Ein HeilbronnSatz für Kettenbrüche mit
ungeraden Teilnennern, Math. Nachr. 101 (1981),
295–307 (German). MR 638347
(83c:10011), http://dx.doi.org/10.1002/mana.19811010126
 [8]
, On the metrical theory of continued fractions with odd partial quotients, in print.
 [9]
F. Schweiger, Continued fractions with odd and even partial quotients, Arbeitsbericht of Math. Instit. der Univ. Salzburg 4 (1982), 5970.
 [10]
Eduard
Wirsing, On the theorem of GaussKusminLévy and a
Frobeniustype theorem for function spaces, Acta Arith.
24 (1973/74), 507–528. Collection of articles
dedicated to Carl Ludwig Siegel on the occasion of his seventyfifth
birthday, V. MR
0337868 (49 #2637)
 [1]
 S. Grigorescu and M. Iosifescu, Dependence with complete connections and applications, Ed. Stiintifica & Encicloped., Bucharest, 1982. MR 692365 (85d:60102)
 [2]
 M. Iosifescu and R. Theodorescu, Random processes and learning, SpringerVerlag, New York, 1969. MR 0293704 (45:2781)
 [3]
 M. Kac, Statistical independence in probability analysis, and number theory, Carus Math. Monograph, vol. 12, Math. Assoc. of Amer., Washington, D.C., 1959. MR 0110114 (22:996)
 [4]
 S. Kalpazidou, Some asymptotic results on digits of the nearest integer fraction, J. Number Theory (to appear). MR 831872 (87i:11101)
 [5]
 , On a random system with complete connections associated with the continued fraction to the nearer integer expansion, Rev. Roumaine Math. Pures Appl. 7 (1985), 527537. MR 826234 (87i:11100)
 [6]
 M. F. Norman, Markov processes and learning models, Academic Press, New York, 1972. MR 0423546 (54:11522)
 [7]
 G. J. Rieger, Ein HilbronnSatz für Kettenbrüche mit ungeraden Teilnernnern, Math. Nachr. 101 (1981), 295307. MR 638347 (83c:10011)
 [8]
 , On the metrical theory of continued fractions with odd partial quotients, in print.
 [9]
 F. Schweiger, Continued fractions with odd and even partial quotients, Arbeitsbericht of Math. Instit. der Univ. Salzburg 4 (1982), 5970.
 [10]
 E. Wirsing, On the theorem of GaussKusminLévy and a Frobeniustype theorem for function spaces, Acta Arith. 24 (1974), 507528. MR 0337868 (49:2637)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198608264936
PII:
S 00029939(1986)08264936
Article copyright:
© Copyright 1986
American Mathematical Society
