A Gaussian measure for certain continued fractions

A Gaussian measure for certain continued fractions
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by Sofia Kalpazidou PDF

Proc. Amer. Math. Soc. 96 (1986), 629-635 Request permission

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

References

Şerban Grigorescu and Marius Iosifescu, Dependenţă cu legături complete şi aplicaţii, Editura Ştiinţifică si Enciclopedicǎ, Bucharest, 1982 (Romanian). With an English summary. MR 692365
M. Iosifescu and R. Theodorescu, Random processes and learning, Die Grundlehren der mathematischen Wissenschaften, Band 150, Springer-Verlag, New York, 1969. MR 0293704
Mark Kac, Statistical independence in probability, analysis and number theory. , The Carus Mathematical Monographs, No. 12, Mathematical Association of America; distributed by John Wiley and Sons, Inc., New York, 1959. MR 0110114
Sofia Kalpazidou, Some asymptotic results on digits of the nearest integer continued fraction, J. Number Theory 22 (1986), no. 3, 271–279. MR 831872, DOI 10.1016/0022-314X(86)90011-9
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
M. Frank Norman, Markov processes and learning models, Mathematics in Science and Engineering, Vol. 84, Academic Press, New York-London, 1972. MR 0423546
G. J. Rieger, Ein Heilbronn-Satz für Kettenbrüche mit ungeraden Teilnennern, Math. Nachr. 101 (1981), 295–307 (German). MR 638347, DOI 10.1002/mana.19811010126

On the metrical theory of continued fractions with odd partial quotients

Continued fractions with odd and even partial quotients

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Eduard Wirsing, On the theorem of Gauss-Kusmin-Lévy and a Frobenius-type theorem for function spaces, Acta Arith. 24 (1973/74), 507–528. MR 337868, DOI 10.4064/aa-24-5-507-528