Lower bounds for resultants, I

J. H. Evertse; K. Györy

Compositio Mathematica (1993)

  • Volume: 88, Issue: 1, page 1-23
  • ISSN: 0010-437X

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Evertse, J. H., and Györy, K.. "Lower bounds for resultants, I." Compositio Mathematica 88.1 (1993): 1-23. <http://eudml.org/doc/90238>.

@article{Evertse1993,
author = {Evertse, J. H., Györy, K.},
journal = {Compositio Mathematica},
keywords = {binary forms; resultant; lower bounds; rings of -integers; resultant inequalities; Thue-Mahler inequalities},
language = {eng},
number = {1},
pages = {1-23},
publisher = {Kluwer Academic Publishers},
title = {Lower bounds for resultants, I},
url = {http://eudml.org/doc/90238},
volume = {88},
year = {1993},
}

TY - JOUR
AU - Evertse, J. H.
AU - Györy, K.
TI - Lower bounds for resultants, I
JO - Compositio Mathematica
PY - 1993
PB - Kluwer Academic Publishers
VL - 88
IS - 1
SP - 1
EP - 23
LA - eng
KW - binary forms; resultant; lower bounds; rings of -integers; resultant inequalities; Thue-Mahler inequalities
UR - http://eudml.org/doc/90238
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. Zbl0248.12002MR306119
  2. [2] J.H. Evertse, On equations in S-units and the Thue-Mahler equation, Invent. Math.75 (1984), 561-584. Zbl0521.10015MR735341
  3. [3] J.H. Evertse, On sums of S-units and linear recurrences, Compositio Math.53 (1984) 225-244. Zbl0547.10008MR766298
  4. [4] J.H. Evertse and K. Györy, Thue-Mahler equations with a small number of solutions, J. Reine Angew. Math.399 (1989) 60-80. Zbl0675.10009MR1004133
  5. [5] J.H. Evertse and K. Györy, Effective finiteness results for binary forms with given discriminant, Compositio Math.79 (1991) 169-204. Zbl0746.11020MR1117339
  6. [6] J H. Evertse, K. Györy, C. L. Stewart and R. Tijdeman, On S-unit equations in two unknowns, Invent. Math.92 (1988), 461-477. Zbl0662.10012MR939471
  7. [7] K. Györy, Sur les polynômes à coefficients entiers et de discriminant donné, Acta Arith.23 (1973) 419-426. Zbl0269.12001MR437489
  8. [8] K. Györy, On polynomials with integer coefficients and given discriminant, V, p-adic generalizations, Acta Math. Acad. Sci. Hungar.32 (1978), 175-190. Zbl0402.10053MR498497
  9. [9] K. Györy, On arithmetic graphs associated with integral domains, in: A Tribute to Paul Erdös (eds. A. Baker, B. Bollobás, A. Hajnal), pp. 207-222. Cambridge University Press, 1990. Zbl0727.11039MR1117015
  10. [10] K. Györy, On the number of pairs of polynomials with given resultant or given semi-resultant, to appear. Zbl0798.11043MR1243304
  11. [11] M. Laurent, Equations diophantiennes exponentielles, Invent. Math.78 (1984) 299-327. Zbl0554.10009MR767195
  12. [12] H.P. Schlickewei, The p-adic Thue-Siegel-Roth-Schmidt theorem, Archiv der Math.29 (1977) 267-270. Zbl0365.10026MR491529
  13. [13] W.M. Schmidt, Inequalities for resultants and for decomposable forms, in: Diophantine Approximation and its Applications (ed. C. F. Osgood), pp. 235-253, Academic Press, New York, 1973. Zbl0267.10023MR354566
  14. [14] W.M. Schmidt, Diophantine Approximation, Lecture Notes in Math. 785, Springer-Verlag, 1980. Zbl0421.10019MR568710
  15. [15] E. Wirsing, On approximations of algebraic numbers by algebraic numbers of bounded degree, in: Proc. Symp. Pure Math. 20 (1969 Number Theory Institute; ed. D. J. Lewis), pp. 213-247, Amer. Math. Soc., Providence, 1971. Zbl0223.10017MR319929

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