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ArticleOriginal scientific text

Title

The number of families of solutions of decomposable form equations

Authors 1, 2

Affiliations

  1. Mathematical Institute, University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands
  2. Mathematical Institute, Kossuth Lajos University, P.O. Box 12, 4010 Debrecen, Hungary

Bibliography

  1. Z. I. Borevich and I. R. Shafarevich, Number Theory, Academic Press, New York, 1967.
  2. G. R. Everest, On the solution of the norm form equation, Amer. J. Math. 114 (1992), 667-681; Addendum, Amer. J. Math., 787-788.
  3. G. R. Everest and K. Győry, Counting solutions of decomposable form equations, Acta Arith. 79 (1997), 173-191.
  4. J.-H. Evertse, The number of solutions of decomposable form equations, Invent. Math. 122 (1995), 559-601.
  5. K. Győry, On the numbers of families of solutions of systems of decomposable form equations, Publ. Math. Debrecen 42 (1993), 65-101.
  6. K. Győry und A. Pethő, Über die Verteilung der Lösungen von Normformen Gleichungen II, Acta Arith. 32 (1977), 349-363.
  7. K. Győry und A. Pethő, Über die Verteilung der Lösungen von Normformen Gleichungen III, Acta Arith. 37 (1980), 143-165.
  8. S. Lang, Fundamentals of Diophantine Geometry, Springer, Berlin, 1983.
  9. M. Laurent, Equations diophantiennes exponentielles, Invent. Math. 78 (1984), 299-327.
  10. D. G. Northcott, An inequality in the theory of arithmetic on algebraic varieties, Proc. Cambridge Philos. Soc. 45 (1949), 502-509.
  11. D. G. Northcott, A further inequality in the theory of arithmetic on algebraic varieties, Proc. Cambridge Philos. Soc., 510-518.
  12. A. Pethő, Über die Verteilung der Lösungen von S-Normformen Gleichungen, Publ. Math. Debrecen 29 (1982), 1-17.
  13. H. P. Schlickewei, On norm form equations, J. Number Theory 9 (1977), 370-380.
  14. H. P. Schlickewei, S-unit equations over number fields, Invent. Math. 102 (1990), 95-107.
  15. W. M. Schmidt, Linearformen mit algebraischen Koeffizienten II, Math. Ann. 191 (1971), 1-20.
  16. W. M. Schmidt, Norm form equations, Ann. of Math. 96 (1972), 525-551.
  17. W. M. Schmidt, The number of solutions of norm form equations, Trans. Amer. Math. Soc. 317 (1990), 197-227.
  18. P. M. Voutier, Effective and quantitative results on integral solutions of certain classes of Diophantine equations, Ph.D. Thesis, University of Colorado at Boulder, 1993.
Acta Arithmetica
1997/80/4
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Pages:
367-394
Main language of publication
English
Received
1997-01-16
Published
1997
Exact and natural sciences