On approximation of real numbers by real algebraic numbers

V. Beresnevich

Acta Arithmetica (1999)

  • Volume: 90, Issue: 2, page 97-112
  • ISSN: 0065-1036

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V. Beresnevich. "On approximation of real numbers by real algebraic numbers." Acta Arithmetica 90.2 (1999): 97-112. <http://eudml.org/doc/207323>.

@article{V1999,
author = {V. Beresnevich},
journal = {Acta Arithmetica},
keywords = {approximation of real algebraic numbers by real algebraic numbers; planar curves},
language = {eng},
number = {2},
pages = {97-112},
title = {On approximation of real numbers by real algebraic numbers},
url = {http://eudml.org/doc/207323},
volume = {90},
year = {1999},
}

TY - JOUR
AU - V. Beresnevich
TI - On approximation of real numbers by real algebraic numbers
JO - Acta Arithmetica
PY - 1999
VL - 90
IS - 2
SP - 97
EP - 112
LA - eng
KW - approximation of real algebraic numbers by real algebraic numbers; planar curves
UR - http://eudml.org/doc/207323
ER -

References

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  1. [1] A. Baker, On a theorem of Sprindžuk, Proc. Roy. Soc. London Ser. A 292 (1966), 92-104. Zbl0146.06302
  2. [2] A. Baker and W. Schmidt, Diophantine approximation and Hausdorff dimension, Proc. London Math. Soc. 21 (1970), 1-11. Zbl0206.05801
  3. [3] R. Baker, Sprindžuk's theorem and Hausdorff dimension, Mathematika 23 (1976), 184-196. Zbl0343.10018
  4. [4] V. Beresnevich, Effective measure estimates for sets of real numbers with a given error of approximation by quadratic irrationalities, Vestsi Akad. Navuk Belarusi Ser. Fiz. Mat. Navuk 1996, no. 4, 10-15 (in Russian). Zbl0871.11049
  5. [5] V. Beresnevich, V. Bernik and M. Dodson, Inhomogeneous non-linear Diophantine approximation, in: Papers in honor of Sprindžuk's 60th birthday, Minsk, 1997, 13-20. 
  6. [6] V. Bernik, On the best approximation of zero by values of integral polynomials, Acta Arith. 53 (1989), 17-28 (in Russian). Zbl0692.10042
  7. [7] V. Bernik, Asymptotic behavior of the number of solutions for some systems of inequalities in the theory of Diophantine approximation of dependent quantities, Vestsi Akad. Navuk BSSR Ser. Fiz. Mat. Navuk 1973, no. 1, 10-17 (in Russian). 
  8. [8] M. M. Dodson, B. P. Rynne and J. A. G. Vickers, Khinchine-type theorems on manifolds, Acta Arith. 57 (1991), 115-130. Zbl0736.11040
  9. [9] A. Khintchine [A. Khinchin], Continued Fractions, University of Chicago Press, 1964. Zbl0117.28601
  10. [10] D. Y. Kleinbock and G. A. Margulis, Flows on homogeneous spaces and Diophantine approximation on manifolds, preprint 97-108, SF 343 Diskrete Strukturen in der Mathematik, Universität Bielefeld. 
  11. [11] J. Koksma, Über die Mahlersche Klasseneinteilung der transzendenten Zahlen und die Approximation komplexer Zahlen durch algebraische Zahlen, Monatsh. Math. Phys. 48 (1939), 176-189. Zbl0021.20804
  12. [12] K. Mahler, Über das Maß der Menge aller S-Zahlen, Math. Ann. 106 (1932), 131-139. 
  13. [13] K. Mahler, Zur Approximation der Exponentialfunktion und des Logarithmus, Teil I, J. Reine Angew. Math. 166 (1932), 118-150. Zbl0003.38805
  14. [14] W. Schmidt, Diophantine Approximation, Springer, Berlin, 1980. Zbl0421.10019
  15. [15] V. Sprindžuk, More on Mahler's conjecture, Soviet Math. Dokl. 5 (1964), 361-363. 
  16. [16] V. Sprindžuk, The proof of Mahler's conjecture on the measure of the set of S-numbers, Izv. Akad. Nauk SSSR Math. Series 19 (1965), 191-194 (in Russian). 
  17. [17] V. Sprindžuk, Mahler's Problem in the Metric Theory of Numbers, Transl. Math. Monographs 25, Amer. Math. Soc., Providence, R.I., 1969. 
  18. [18] V. Sprindžuk, Metric Theory of Diophantine Approximation, Wiley, New York, 1979. Zbl0306.10037
  19. [19] E. Wirsing, Approximation mit algebraischen Zahlen beschränkten Grades, J. Reine Angew. Math. 206 (1961), 67-77. Zbl0097.03503

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