Cite

[B] BOURGAIN, J.: Exponential sum estimates over subgroups ofZq×Z_q^ \times, q arbitrary, J. Anal. Math. 97 (2005), 317–356.10.1007/BF02807410Search in Google Scholar

[BFR] BRODERICK, R.–FISHMAN, L.–REICH, A.: Intrinsic Approximation on Cantor-like Sets, a Problem of Mahler, Mosc. J. Comb. Number Theory 1 (2011), 3–12.Search in Google Scholar

[Bu] BUGEAUD, Y.: Diophantine approximation and Cantor sets, Math. Ann. 341 (2008), no. 3, 677–684.Search in Google Scholar

[E] ERDŐS, P.: On the sumd|2n−1d−1, Israel J. Math. 9 (1971), 43–48.10.1007/BF02771618Search in Google Scholar

[F] FISHMAN, L.: Schmidt’s game on fractals, Israel J. Math. 171 (2009), 77–92.10.1007/s11856-009-0041-xSearch in Google Scholar

[FS] FISHMAN, L.—SIMMONS, D.: Intrinsic approximation for fractals defined by rational iterated function systems: Mahler’s research suggestion, Proc. Lond. Math. Soc.(3) 109 (2014), no. 1, 189–212.Search in Google Scholar

[LSV] LEVESLEY, J.—SALP, C.—VELANI, S.: On a problem of K. Mahler: Diophantine approximation and Cantor sets, Math. Ann. 338 (2007), no. 1, 97–118.Search in Google Scholar

[M] MAHLER, K.: Some suggestions for further research, Bull. Aust. Math. Soc. 29 (1984), no. 1, 101–108.Search in Google Scholar

[Mo] MOREE, P.: Artin’s primitive root conjecture — a survey, Integers 12 (2012), no. 6, 1305–1416.Search in Google Scholar

[Sch] SCHLEISCHITZ, J.: On intrinsic and extrinsic rational approximation to Cantor sets, Ergodic Theory and Dynamical Systems (2020), 1–30. (DOI:10.1017/etds.2020.7).Search in Google Scholar

[S] SHPARLINSKI, I.: On the arithmetic structure of rational numbers in the Cantor set, Bull. Aust. Math. Soc. (2020), 1–6 (doi:10.1017/S0004972720000386).Search in Google Scholar

[SW] SIMMONS, D.—WEISS, B.: Random walks on homogeneous spaces and Diophantine approximation on fractals, Invent. Math. 216 (2019), 337–394.10.1007/s00222-019-00856-7Search in Google Scholar

[T] TRAUTHWEIN, T.: Approximation of Cantor Rational Cardinalities by Primitive Words, Master 1 project report (2019), Experimental Mathematics Lab, University of Luxembourg, http://math.uni.lu/eml/projects/reports/Cantor_rationals_project_report.pdfSearch in Google Scholar

[W] WEISS, B.: Almost no points on a Cantor set are very well approximable, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 457 (2001), 949–952.10.1098/rspa.2000.0700Search in Google Scholar

eISSN:
2309-5377
Language:
English