Hausdorff dimension and a generalized form of simultaneous Diophantine approximation

B. P. Rynne; H. Dickinson

Acta Arithmetica (2000)

  • Volume: 93, Issue: 1, page 21-36
  • ISSN: 0065-1036

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B. P. Rynne, and H. Dickinson. "Hausdorff dimension and a generalized form of simultaneous Diophantine approximation." Acta Arithmetica 93.1 (2000): 21-36. <http://eudml.org/doc/207397>.

@article{B2000,
author = {B. P. Rynne, H. Dickinson},
journal = {Acta Arithmetica},
keywords = {Hausdorff dimension; simultaneous homogeneous linear approximation; metric diophantine approximation},
language = {eng},
number = {1},
pages = {21-36},
title = {Hausdorff dimension and a generalized form of simultaneous Diophantine approximation},
url = {http://eudml.org/doc/207397},
volume = {93},
year = {2000},
}

TY - JOUR
AU - B. P. Rynne
AU - H. Dickinson
TI - Hausdorff dimension and a generalized form of simultaneous Diophantine approximation
JO - Acta Arithmetica
PY - 2000
VL - 93
IS - 1
SP - 21
EP - 36
LA - eng
KW - Hausdorff dimension; simultaneous homogeneous linear approximation; metric diophantine approximation
UR - http://eudml.org/doc/207397
ER -

References

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  1. [1] A. S. Besicovitch, Sets of fractional dimension (IV): On rational approximation to real numbers, J. London Math. Soc. 9 (1934), 126-131. Zbl0009.05301
  2. [2] I. Borosh and A. S. Fraenkel, A generalization of Jarník's theorem on Diophantine approximations, Indag. Math. 34 (1972), 193-201. Zbl0242.10014
  3. [3] J. D. Bovey and M. M. Dodson, The Hausdorff dimension of systems of linear forms, Acta Arith. 45 (1986), 337-358. Zbl0534.10025
  4. [4] M. M. Dodson, Hausdorff dimension, lower order and Khintchine's theorem in metric Diophantine approximation, J. Reine Angew. Math. 432 (1992), 69-76. Zbl0749.11036
  5. [5] M. M. Dodson and J. A. G. Vickers, Exceptional sets in Kolmogorov-Arnol'd-Moser theory, J. Phys. A 19 (1986), 349-374. Zbl0605.34041
  6. [6] . R. Dombrovski, Simultaneous approximations of real numbers by algebraic numbers of bounded degree, Dokl. Akad. Nauk BSSR 33 (1989), 205-208. Zbl0676.10040
  7. [7] H. G. Eggleston, Sets of fractional dimension which occur in some problems in number theory, Proc. London Math. Soc. 54 (1952), 42-93. Zbl0045.16603
  8. [8] V. Jarník, Diophantische Approximationen und Hausdorffsches Mass, Mat. Sb. 36 (1929), 371-382. Zbl55.0719.01
  9. [9] V. Jarník, Über die simultanen Diophantischen Approximationen, Math. Z. 33 (1931), 503-543. Zbl57.1370.01
  10. [10] B. P. Rynne, The Hausdorff dimension of certain sets arising from Diophantine approximation by restricted sequences of integer vectors, Acta Arith. 61 (1992), 69-81. Zbl0749.11037
  11. [11] B. P. Rynne, Hausdorff dimension and generalized Diophantine approximation, Bull. London Math. Soc. 30 (1998), 365-376. Zbl0984.11038
  12. [12] V. G. Sprindžuk, Metric Theory of Diophantine Approximations (translated by R. A. Silverman), Winston, Washington, 1979. Zbl0287.10043

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