The number of families of solutions of decomposable form equations

J.-H. Evertse; K. Győry

Acta Arithmetica (1997)

  • Volume: 80, Issue: 4, page 367-394
  • ISSN: 0065-1036

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J.-H. Evertse, and K. Győry. "The number of families of solutions of decomposable form equations." Acta Arithmetica 80.4 (1997): 367-394. <http://eudml.org/doc/207049>.

@article{J1997,
author = {J.-H. Evertse, K. Győry},
journal = {Acta Arithmetica},
keywords = {norm form equations; number of solutions; decomposable form equations},
language = {eng},
number = {4},
pages = {367-394},
title = {The number of families of solutions of decomposable form equations},
url = {http://eudml.org/doc/207049},
volume = {80},
year = {1997},
}

TY - JOUR
AU - J.-H. Evertse
AU - K. Győry
TI - The number of families of solutions of decomposable form equations
JO - Acta Arithmetica
PY - 1997
VL - 80
IS - 4
SP - 367
EP - 394
LA - eng
KW - norm form equations; number of solutions; decomposable form equations
UR - http://eudml.org/doc/207049
ER -

References

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  1. [1] Z. I. Borevich and I. R. Shafarevich, Number Theory, Academic Press, New York, 1967. 
  2. [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. Zbl0755.11012
  3. [3] G. R. Everest and K. Győry, Counting solutions of decomposable form equations, Acta Arith. 79 (1997), 173-191. Zbl0883.11015
  4. [4] J.-H. Evertse, The number of solutions of decomposable form equations, Invent. Math. 122 (1995), 559-601. Zbl0851.11019
  5. [5] K. Győry, On the numbers of families of solutions of systems of decomposable form equations, Publ. Math. Debrecen 42 (1993), 65-101. Zbl0792.11004
  6. [6] K. Győry und A. Pethő, Über die Verteilung der Lösungen von Normformen Gleichungen II, Acta Arith. 32 (1977), 349-363. Zbl0314.12015
  7. [7] K. Győry und A. Pethő, Über die Verteilung der Lösungen von Normformen Gleichungen III, Acta Arith. 37 (1980), 143-165. Zbl0387.10010
  8. [8] S. Lang, Fundamentals of Diophantine Geometry, Springer, Berlin, 1983. Zbl0528.14013
  9. [9] M. Laurent, Equations diophantiennes exponentielles, Invent. Math. 78 (1984), 299-327. 
  10. [10] D. G. Northcott, An inequality in the theory of arithmetic on algebraic varieties, Proc. Cambridge Philos. Soc. 45 (1949), 502-509. Zbl0035.30701
  11. [11] D. G. Northcott, A further inequality in the theory of arithmetic on algebraic varieties, Proc. Cambridge Philos. Soc., 510-518. Zbl0035.30701
  12. [12] A. Pethő, Über die Verteilung der Lösungen von S-Normformen Gleichungen, Publ. Math. Debrecen 29 (1982), 1-17. 
  13. [13] H. P. Schlickewei, On norm form equations, J. Number Theory 9 (1977), 370-380. Zbl0365.10016
  14. [14] H. P. Schlickewei, S-unit equations over number fields, Invent. Math. 102 (1990), 95-107. Zbl0711.11017
  15. [15] W. M. Schmidt, Linearformen mit algebraischen Koeffizienten II, Math. Ann. 191 (1971), 1-20. Zbl0198.07103
  16. [16] W. M. Schmidt, Norm form equations, Ann. of Math. 96 (1972), 525-551. Zbl0226.10024
  17. [17] W. M. Schmidt, The number of solutions of norm form equations, Trans. Amer. Math. Soc. 317 (1990), 197-227. Zbl0693.10014
  18. [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. 

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