An improvement of the quantitative subspace theorem

Jan-Hendrik Evertse

Compositio Mathematica (1996)

  • Volume: 101, Issue: 3, page 225-311
  • ISSN: 0010-437X

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Evertse, Jan-Hendrik. "An improvement of the quantitative subspace theorem." Compositio Mathematica 101.3 (1996): 225-311. <http://eudml.org/doc/90444>.

@article{Evertse1996,
author = {Evertse, Jan-Hendrik},
journal = {Compositio Mathematica},
keywords = {linear forms with algebraic coefficients; subspace theorem; number of solutions of norm form equations; -unit equations; decomposable form equations; Roth's lemma; Dyson's lemma},
language = {eng},
number = {3},
pages = {225-311},
publisher = {Kluwer Academic Publishers},
title = {An improvement of the quantitative subspace theorem},
url = {http://eudml.org/doc/90444},
volume = {101},
year = {1996},
}

TY - JOUR
AU - Evertse, Jan-Hendrik
TI - An improvement of the quantitative subspace theorem
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 101
IS - 3
SP - 225
EP - 311
LA - eng
KW - linear forms with algebraic coefficients; subspace theorem; number of solutions of norm form equations; -unit equations; decomposable form equations; Roth's lemma; Dyson's lemma
UR - http://eudml.org/doc/90444
ER -

References

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  1. 1 Bombieri, E. and van der Poorten, A.J.: Some quantitative results related to Roth's theorem, J. Austral. Math. Soc. (Ser. A) 45 (1988), 233-248, Corrigenda, ibid, 48 (1990), 154-155. Zbl0697.10028MR1026847
  2. 2 Bombieri, E. and Vaaler, J.: On Siegel's Lemma, Invent. Math.73 (1983), 11-32. Zbl0533.10030MR707346
  3. 3 Esnault, H. and Viehweg, E.: Dyson's Lemma for polynomials in several variables (and the theorem of Roth), Invent. Math.78 (1984), 445-490. Zbl0545.10021MR768988
  4. 4 Evertse, J.-H.: On equations in S-units and the Thue-Mahler equation, Invent. Math.75, 561-584. Zbl0521.10015MR735341
  5. 5 Evertse, J.-H.: The Subspace theorem of W.M. Schmidt, in: Diophantine approximation and abelian varieties, Edixhoven, B., Evertse, J.-H., eds. Lecture Notes Math.1566, Springer Verlag, Berlin etc. 1993, Chap. IV. Zbl0812.11039MR1289002
  6. 6 Evertse, J.-H.: An explicit version of Faltings' Product theorem and an improvement of Roth's lemma, Acta Arith. 73 (1995), 215-248. Zbl0857.11034MR1364461
  7. 7 Faltings, G.: Diophantine approximation on abelian varieties, Annals of Math.133 (1991), 549-576. Zbl0734.14007MR1109353
  8. 8 Faltings, G. and Wüstholz, G.: Diophantine approximations on projective spaces, Invent. Math.116 (1994), 109-138. Zbl0805.14011MR1253191
  9. 9 Gross, R.: A note on Roth's theorem, J. of Number Theory36 (1990), 127-132. Zbl0722.11034MR1068678
  10. 10 Lang, S.: Algebraic Number Theory, Addison-Wesley, Reading, Massachusetts, 1970. Zbl0211.38404MR282947
  11. 11 McFeat, R.B.: Geometry of numbers in adele spaces, Dissertationes Mathematicae 88, PWN Polish Scient. Publ., Warsaw, 1971. Zbl0229.10014MR318104
  12. 12 Mahler, K.: Inequalities for ideal bases in algebraic number fields, J. Austral. Math. Soc.4 (1964), 425-448. Zbl0218.12004MR176975
  13. 13 Roth, K.F.: Rational approximations to algebraic numbers, Mathematika2 (1955), 1-20. Zbl0064.28501MR72182
  14. 14 Schlickewei, H.P.: The p-adic Thue-Siegel-Roth-Schmidt theorem, Arch. Math.29 (1977), 267-270. Zbl0365.10026MR491529
  15. 15 Schlickewei, H.P.: The number of subspaces occurring in the p-adic Subspace Theorem in Diophantine approximation, J. reine angew. Math.406 (1990), 44-108. Zbl0693.10027MR1048236
  16. 16 Schlickewei, H.P.: The quantitative Subspace Theorem for number fields, Compositio Math.82 (1992), 245-273. Zbl0751.11033MR1163217
  17. 17 Schmidt, W.M.: Norm form equations, Annals of Math.96 (1972), 526-551. Zbl0226.10024MR314761
  18. 18 Schmidt, W.M.: Diophantine approximation, Lecture Notes in Math. 785, Springer Verlag, Berlin etc., 1980 Zbl0421.10019MR568710
  19. 19 Schmidt, W.M.: The subspace theorem in diophantine approximations, Compositio Math.69 (1989), 121-173. Zbl0683.10027MR984633
  20. 20 Silverman, J.H.: Lower bounds for height functions, Duke Math. J.51 (1984), 395-403. Zbl0579.14035MR747871
  21. 21 Stark, H.M.: Some effective cases of the Brauer-Siegel Theorem, Invent. Math.23 (1974), 135-152. Zbl0278.12005MR342472

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