Geodesic
On the distribution of prime denominators of the approximants for almost all real numbers
Izvestiya. Mathematics , Tome 72 (2008) no. 2, pp. 265-282.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove an asymptotic formula for the distribution of primes among the denominators of the approximants for almost all real numbers. 
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V. A. Bykovskii. On the distribution of prime denominators of the approximants for almost all real numbers. Izvestiya. Mathematics , Tome 72 (2008) no. 2, pp. 265-282. http://geodesic.mathdoc.fr/item/IM2_2008_72_2_a2/

[1] K. Prachar, Primzahlverteilung, Springer-Verlag, Berlin–Göttingen–Heidelberg, 1957 | MR | MR | Zbl | Zbl

[2] “Iz «lyubitelskikh zadach» A. D. Sakharova”, Kvant, 1991, no. 5, 11–12

[3] C. Hooley, Applications of sieve methods to the theory of numbers, Cambridge Tracts in Mathematics, 70, Cambridge University Press, Cambridge–New York–Melbourne, 1976 | MR | MR | Zbl | Zbl

[4] G. Harman, “Metrical theorems on prime values of the integer parts of real sequences”, Proc. London Math. Soc. (3), 75:3 (1997), 481–496 | DOI | MR | Zbl

[5] P. Rowe, “Metrical results on sums of squares and prime values of the integer parts of sequences”, Acta Arith., 118:2 (2005), 101–115 | DOI | MR | Zbl

[6] A. Khintchine, “Zur metrischen Kettenbruchtheorie”, Compositio Math., 3 (1936), 276–285 | MR | Zbl

[7] P. Lévy, “Sur le développement en fraction continue d'un nombre choisi au hasard”, Compositio Math., 3 (1936), 286–303 | MR | Zbl

[8] V. G. Sprindzhuk, Metricheskaya teoriya diofantovykh priblizhenii, Nauka, M., 1977 | MR | Zbl

[9] G. Harman, “Metric Diophantine approximation with two restricted variables. I. Two square-free integers, or integers in arithmetic progressions”, Math. Proc. Cambridge Philos. Soc., 103:2 (1988), 197–206 | DOI | MR | Zbl

[10] I. V. Arnold, Teoriya chisel, Gos. izd-vo Narkomprosa RSFSR, M., 1939

[11] A. V. Ustinov, “On statistical properties of finite continued fractions”, J. Math. Sci., 137:2 (2006), 4722–4738 | DOI | MR | Zbl

[12] V. A. Bykovskii, “Otsenka dispersii dlin konechnykh nepreryvnykh drobei”, Fundament. i prikl. matem., 11:6 (2005), 15–26 | MR

[13] H. L. Montgomery, Topics in multiplicative number theory, Lecture Notes in Math., 227, Springer-Verlag, Berlin–New York, 1971 | MR | MR | Zbl | Zbl