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Zaremba’s Conjecture for Geometric Sequences: An Algorithm

Pages 530-535 | Received 24 Aug 2023, Accepted 10 Oct 2023, Published online: 02 Apr 2024

References

  • Zaremba SK. La Méthode des “Bons Treillis” pour le Calcul des Intégrales multiples. In: Applications of Number Theory to Numerical Analysis. (Proc. Sympos., Univ. Montreal, Montreal); 1972. p. 39–119.
  • Bourgain J, Kontorovich A. On Zaremba’s conjecture. Ann Math. (2) 2014;180(1):137–196. doi: 10.4007/annals.2014.180.1.3.
  • Huang S. An improvement to Zaremba’s conjecture. Geom Funct Anal. 2015;25(3):860–914. doi: 10.1007/s00039-015-0327-6.
  • Kontorovich A. From Apollonius to Zaremba: local-global phenomena in thin orbits. Bull Amer Math Soc. (N.S.) 2013;50(2):187–228. doi: 10.1090/S0273-0979-2013-01402-2.
  • Niederreiter H. Dyadic fractions with small partial quotients. Monatsh Math. 1986;101:309–315. doi: 10.1007/BF01559394.
  • Yodphotong M, Laohakosol V. Proofs of Zaremba’s conjecture for powers of 6. In: Proceedings of the International Conference on Algebra and Its Applications (ICAA 2002) (Bangkok); 2002. p. 278–282.
  • Kan ID, Krotkova NA. Quantitative generalizations of Niederreiter’s results on continued fractions. Chebyshevskĭi Sb. 2011;12(1):100–119.
  • Shulga N. Radical bound for Zaremba’s conjecture. arXiv:2310.09801. doi: 10.48550/arXiv.2310.09801.
  • Mendès France M. Sur les fractions continues limitées. Acta Arith. 1973;23(2):207–215. doi: 10.4064/aa-23-2-207-215.
  • van der Poorten AJ, Shallit J. Folded continued fractions. J Number Theory. 1992;40(2):237–250. doi: 10.1016/0022-314x(92)90042-n.
  • Komatsu T. On a Zaremba’s conjecture for powers. Sarajevo J Math. 2005;1(13):9–13.

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