Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A Gaussian measure for certain continued fractions

Author: Sofia Kalpazidou
Journal: Proc. Amer. Math. Soc. 96 (1986), 629-635
MSC: Primary 11K50; Secondary 28D99
MathSciNet review: 826493
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We solve a variant of Gauss' problem for grotesque continued fraction using the approach of dependence with complete connections.

References [Enhancements On Off] (What's this?)

  • [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
  • [2] M. Iosifescu and R. Theodorescu, Random processes and learning, Springer-Verlag, New York, 1969. Die Grundlehren der mathematischen Wissenschaften, Band 150. MR 0293704
  • [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
  • [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,
  • [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
  • [6] M. Frank Norman, Markov processes and learning models, Academic Press, New York-London, 1972. Mathematics in Science and Engineering, Vol. 84. MR 0423546
  • [7] G. J. Rieger, Ein Heilbronn-Satz für Kettenbrüche mit ungeraden Teilnennern, Math. Nachr. 101 (1981), 295–307 (German). MR 638347,
  • [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), 59-70.
  • [10] Eduard Wirsing, On the theorem of Gauss-Kusmin-Lévy and a Frobenius-type theorem for function spaces, Acta Arith. 24 (1973/74), 507–528. Collection of articles dedicated to Carl Ludwig Siegel on the occasion of his seventy-fifth birthday, V. MR 0337868,

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11K50, 28D99

Retrieve articles in all journals with MSC: 11K50, 28D99

Additional Information

Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society