The quantitative subspace theorem for number fields

Hans Peter Schlickewei

Compositio Mathematica (1992)

  • Volume: 82, Issue: 3, page 245-273
  • ISSN: 0010-437X

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Schlickewei, Hans Peter. "The quantitative subspace theorem for number fields." Compositio Mathematica 82.3 (1992): 245-273. <http://eudml.org/doc/90153>.

@article{Schlickewei1992,
author = {Schlickewei, Hans Peter},
journal = {Compositio Mathematica},
keywords = {simultaneous diophantine approximation; subspace theorem; algebraic number fields},
language = {eng},
number = {3},
pages = {245-273},
publisher = {Kluwer Academic Publishers},
title = {The quantitative subspace theorem for number fields},
url = {http://eudml.org/doc/90153},
volume = {82},
year = {1992},
}

TY - JOUR
AU - Schlickewei, Hans Peter
TI - The quantitative subspace theorem for number fields
JO - Compositio Mathematica
PY - 1992
PB - Kluwer Academic Publishers
VL - 82
IS - 3
SP - 245
EP - 273
LA - eng
KW - simultaneous diophantine approximation; subspace theorem; algebraic number fields
UR - http://eudml.org/doc/90153
ER -

References

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  1. [1] E. Bombieri and A.J. van der Poorten: Some quantitative results related to Roth's theorem, J. Austral. Math. Soc. (series A), 45 (1988), 233-248. Zbl0664.10017MR951583
  2. [2] E. Bombieri and J. Vaaler: On Siegel's lemma, Invent. Math.73 (1983), 11-32. Zbl0533.10030MR707346
  3. [3] J.W.S. Cassels: An introduction to the geometry of numbers, Springer Grundlehren99 (1959). Zbl0086.26203
  4. [4] H. Davenport and K.F. Roth: Rational approximation to algebraic numbers, Mathematika2 (1955), 160-167. Zbl0066.29302MR77577
  5. [5] H. Luckhardt: Herbrand-Analysen zweier Beweise des Satzes von Roth; polynomiale Anzahlschranken, J. of Symb. Logic54 (1989), 234-263. Zbl0669.03024MR987335
  6. [6] K. Mahler: Zur Approximation algebraischer Zahlen I. (Über den gröBten Primteiler binärer Formen), Math. Ann. 107 (1933), 691-730. Zbl0006.10502MR1512822JFM59.0220.01
  7. [7] K.F. Roth: Rational approximations to algebraic numbers, Mathematika2 (1955), 1-20. Zbl0064.28501MR72182
  8. [8] H.P. Schlickewei: On products of special linear forms with algebraic coefficients, Acta Arith.31 (1976), 389-398. Zbl0349.10030MR429784
  9. [9] H.P. Schlickewei: The p-adic Thue-Siegel-Roth-Schmidt theorem, Arch. Math.29 (1977), 267-270. Zbl0365.10026MR491529
  10. [10] H.P. Schlickewei: The number of subspaces occurring in the p-adic subspace theorem in diophantine approximation, J. Reine Angew. Math.406 (1990), 44-108. Zbl0693.10027MR1048236
  11. [11] H.P. Schlickewei: An explicit upper bound for the number of solutions of the S-unit equation, J. Reine Angew. Math.406 (1990), 109-120. Zbl0693.10016MR1048237
  12. [12] H.P. Schlickewei: Linear equations in integers with bounded sum of digits, J. Number Th.35 (1990), 335-344. Zbl0711.11018MR1062338
  13. [13] W.M. Schmidt: Norm form equations, Annals of Math.96 (1972), 526-551. Zbl0226.10024MR314761
  14. [14] W.M. Schmidt: Diophantine approximation, Springer Lecture Notes in Math. 785 (1980). Zbl0421.10019MR568710
  15. [15] W.M. Schmidt: Simultaneous approximation to algebraic numbers by elements of a number field, Monatsh. Math.79 (1975), 55-66. Zbl0317.10042MR364112
  16. [16] W.M. Schmidt: The subspace theorem in diophantine approximations, Comp. Math.69 (1989), 121-173. Zbl0683.10027MR984633
  17. [17] W.M. Schmidt: The number of solutions of norm form equations, Trans. Amer. Math. Soc.317 (1990), 197-227. Zbl0693.10014MR961596
  18. [18] J.H. Silverman: Lower bounds for height functions, Duke Math. J.51 (1984), 395-403. Zbl0579.14035MR747871

Citations in EuDML Documents

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  1. Jan-Hendrik Evertse, An improvement of the quantitative subspace theorem
  2. K. Győry, On the irreducibility of neighbouring polynomials
  3. K. Győry, Some applications of decomposable form equations to resultant equations
  4. Helmut Locher, On the number of good approximations of algebraic numbers by algebraic numbers of bounded degree
  5. Jan-Hendrik Evertse, An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma
  6. K. Győry, A. Sárközy, C. L. Stewart, On the number of prime factors of integers of the form ab + 1

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