The subspace theorem in diophantine approximations

Wolfgang M. Schmidt

Compositio Mathematica (1989)

  • Volume: 69, Issue: 2, page 121-173
  • ISSN: 0010-437X

How to cite


Schmidt, Wolfgang M.. "The subspace theorem in diophantine approximations." Compositio Mathematica 69.2 (1989): 121-173. <>.

author = {Schmidt, Wolfgang M.},
journal = {Compositio Mathematica},
keywords = {rational approximations of algebraic numbers; linear forms; Subspace theorem; quantitative version; upper bound for the number of hyperplanes},
language = {eng},
number = {2},
pages = {121-173},
publisher = {Kluwer Academic Publishers},
title = {The subspace theorem in diophantine approximations},
url = {},
volume = {69},
year = {1989},

AU - Schmidt, Wolfgang M.
TI - The subspace theorem in diophantine approximations
JO - Compositio Mathematica
PY - 1989
PB - Kluwer Academic Publishers
VL - 69
IS - 2
SP - 121
EP - 173
LA - eng
KW - rational approximations of algebraic numbers; linear forms; Subspace theorem; quantitative version; upper bound for the number of hyperplanes
UR -
ER -


  1. 1 E. Bombieri and J. Vaaler, On Siegel's lemma. Invent. Math.73 (1983) 11-32. Zbl0533.10030MR707346
  2. 2 E. Bombieri and A.J. Van der Poorten, Some quantitative results related to Roth's Theorem. MacQuarie Math. Reports, Report No. 87-0005, February 1987. 
  3. 3 J.W.S. Cassels, An Introduction to the Geometry of Numbers. Springer Grundlehren99 (1959). Zbl0086.26203
  4. 4 H. Davenport, Note on a result of Siegel. Acta Arith.2 (1937) 262-265. Zbl63.0922.01JFM63.0922.01
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  6. 6 H. Esnault and E. Viehweg, Dyson's Lemma for polynomials in several variables (and the theorem of Roth). Invent. Math.78 (1984) 445-490. Zbl0545.10021MR768988
  7. 7 J.H. Evertse, Upper bounds for the number of solutions of Diophantine equations. Math. Centrum, Amsterdam (1983) 1-127. Zbl0517.10016MR726562
  8. 8 K. Mahler, Ein Übertragungsprinzip für konvexe Körper. Časopis Pest. Mat. Fys. (1939) 93-102. Zbl0021.10403MR1242JFM65.0175.02
  9. 9 K. Mahler, On compound convex bodies I. Proc. Lon. Math. Soc. (3) 5, 358-379. Zbl0065.28002MR74460
  10. 10 W.M. Schmidt, On heights of algebraic subspaces and diophantine approximations. Annals of Math.83 (1967) 430-472. Zbl0152.03602MR213301
  11. 11 W.M. Schmidt, Norm form equations. Annals of Math.96 (1972) 526-551. Zbl0226.10024MR314761
  12. 12 W.M. Schmidt, The number of solutions of norm form equations. Transactions A.M.S. (to appear). Zbl0693.10014MR961596
  13. 13 W.M. Schmidt, Diophantine approximation. Springer Lecture Notes in Math.785, Berlin, Heidelberg, New York (1980). Zbl0421.10019MR568710

Citations in EuDML Documents

  1. Yann Bugeaud, Extensions of the Cugiani-Mahler theorem
  2. Hans Peter Schlickewei, The quantitative subspace theorem for number fields
  3. Jan-Hendrik Evertse, An improvement of the quantitative subspace theorem
  4. K. Győry, Some applications of decomposable form equations to resultant equations
  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
  7. Yann Bugeaud, Quantitative versions of the Subspace Theorem and applications

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