Effective finiteness theorems for decomposable forms of given discriminant

J. H. Evertse; K. Győry

Acta Arithmetica (1992)

  • Volume: 60, Issue: 3, page 233-277
  • ISSN: 0065-1036

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J. H. Evertse, and K. Győry. "Effective finiteness theorems for decomposable forms of given discriminant." Acta Arithmetica 60.3 (1992): 233-277. <http://eudml.org/doc/206437>.

@article{J1992,
author = {J. H. Evertse, K. Győry},
journal = {Acta Arithmetica},
keywords = {effective finiteness theorems; decomposable forms; -unit equations in two variables},
language = {eng},
number = {3},
pages = {233-277},
title = {Effective finiteness theorems for decomposable forms of given discriminant},
url = {http://eudml.org/doc/206437},
volume = {60},
year = {1992},
}

TY - JOUR
AU - J. H. Evertse
AU - K. Győry
TI - Effective finiteness theorems for decomposable forms of given discriminant
JO - Acta Arithmetica
PY - 1992
VL - 60
IS - 3
SP - 233
EP - 277
LA - eng
KW - effective finiteness theorems; decomposable forms; -unit equations in two variables
UR - http://eudml.org/doc/206437
ER -

References

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  1. [1] B. J. Birch and J. R. Merriman, Finiteness theorems for binary forms with given discriminant, Proc. London Math. Soc. 25 (1972), 385-394. Zbl0248.12002
  2. [2] Z. I. Borevich and I. R. Shafarevich, Number Theory, 2nd ed., Academic Press, New York and London 1967. 
  3. [3] J. H. Evertse, Decomposable form equations with a small linear scattering, to appear. Zbl0754.11009
  4. [4] J. H. Evertse and K. Győry, Decomposable form equations, in: New Advances in Transcendence Theory, A. Baker (ed.), Cambridge University Press, 1988, 175-202. 
  5. [5] J. H. Evertse and K. Győry, Thue-Mahler equations with a small number of solutions, J. Reine Angew. Math. 399 (1989), 60-80. Zbl0675.10009
  6. [6] J. H. Evertse and K. Győry, Effective finiteness results for binary forms with given discriminant, Compositio Math. 79 (1991), 169-204. Zbl0746.11020
  7. [7] J. H. Evertse, K. Győry, C. L. Stewart and R. Tijdeman, S-unit equations and their applications, in: New Advances in Transcendence Theory, A. Baker (ed.), Cambridge University Press, 1988, 110-174. Zbl0658.10023
  8. [8] K. Győry, Sur les polynômes à coefficients entiers et de discriminant donné, Acta Arith. 23 (1973), 419-426. Zbl0269.12001
  9. [9] K. Győry, On polynomials with integer coefficients and given discriminant, V, p-adic generalizations, Acta Math. Acad. Sci. Hungar. 32 (1978), 175-190. Zbl0402.10053
  10. [10] K. Győry, On the number of solutions of linear equations in units of an algebraic number field, Comment. Math. Helv. 54 (1979), 583-600. Zbl0437.12004
  11. [11] K. Győry, On S-integral solutions of norm form, discriminant form and index form equations, Studia Sci. Math. Hungar. 16 (1981), 149-161. Zbl0518.10019
  12. [12] K. Győry, Effective finiteness theorems for polynomials with given discriminant and integral elements with given discriminant over finitely generated domains, J. Reine Angew. Math. 346 (1984), 54-100. Zbl0519.13008
  13. [13] G. J. Janusz, Algebraic Number Fields, Academic Press, New York and London 1973. Zbl0307.12001
  14. [14] I. Kaplansky, Modules over Dedekind rings and valuation rings, Trans. Amer. Math. Soc. 72 (1952), 327-340. Zbl0046.25701
  15. [15] S. Lang, Algebraic Number Theory, Springer, 1970. Zbl0211.38404
  16. [16] K. Mahler, Über die Annäherung algebraischer Zahlen durch periodische Algorithmen, Acta Math. 68 (1937), 109-144. Zbl0017.05701
  17. [17] T. Nagell, Contributions à la théorie des modules et des anneaux algébriques, Ark. Mat. 6 (1965), 161-178. Zbl0132.28304
  18. [18] W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers, Polish Scientific Publishers, Warszawa 1974. Zbl0276.12002
  19. [19] H. M. Stark, Some effective cases of the Brauer-Siegel theorem, Invent. Math. 23 (1974), 135-152. Zbl0278.12005
  20. [20] O. Zariski and P. Samuel, Commutative Algebra, Vol. I, D. Van Nostrand Co., Toronto-New York-London 1958. 

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