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1996 | 74 | 1 | 67-80
Tytuł artykułu

Bounds for the solutions of unit equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
74
Numer
1
Strony
67-80
Opis fizyczny
Daty
wydano
1996
otrzymano
1994-12-27
poprawiono
1995-04-18
Twórcy
autor
  • U. F. R. de Mathématiques, Université Louis Pasteur, 7, rue René Descartes, 67084 Strasbourg, France
  • Institute of Mathematics, Kossuth Lajos University, 4010 Debrecen, Hungary
Bibliografia
  • [1] A. Baker and G. Wüstholz, Logarithmic forms and group varieties, J. Reine Angew. Math. 442 (1993), 19-62.
  • [2] P. E. Blanksby and H. L. Montgomery, Algebraic integers near the unit circle, Acta Arith. 18 (1971), 355-369.
  • [3] E. Bombieri, Effective diophantine approximation on Gₘ, Ann. Scuola Norm. Sup. Pisa (IV) 20 (1993), 61-89.
  • [4] Z. I. Borevich and I. R. Shafarevich, Number Theory, 2nd ed., Academic Press, New York, 1967.
  • [5] B. Brindza, On the generators of S-unit groups in algebraic number fields, Bull. Austral. Math. Soc. 43 (1991), 325-329.
  • [6] J. W. S. Cassels, An Introduction to the Geometry of Numbers, Grundlehren Math. Wiss. 99, Springer, Berlin, 1959.
  • [7] E. Dobrowolski, On the maximal modulus of conjugates of an algebraic integer, Bull. Acad. Polon. Sci. 26 (1978), 291-292.
  • [8] E. Dobrowolski, On a question of Lehmer and the number of irreducible factors of a polynomial, Acta Arith. 34 (1979), 391-401.
  • [9] A. Dubickas, On a conjecture of A. Schinzel and H. Zassenhaus, Acta Arith. 63 (1993), 15-20.
  • [10] J. H. Evertse and K. Győry, Effective finiteness results for binary forms with given discriminant, Compositio Math. 79 (1991), 169-204.
  • [11] 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.
  • [12] E. Friedman, Analytic formulas for regulators of number fields, Invent. Math. 98 (1989), 599-622.
  • [13] K. Győry, On the number of solutions of linear equations in units of an algebraic number field, Comment. Math. Helv. 54 (1979), 583-600.
  • [14] K. Győry, On the solutions of linear diophantine equations in algebraic integers of bounded norm, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 22/23 (1980), 225-233.
  • [15] K. Győry, Résultats effectifs sur la représentation des entiers par des formes décomposables, Queen's Papers in Pure and Appl. Math. 56 (1980).
  • [16] K. Győry, Some recent applications of S-unit equations, in: Journées Arithmétiques de Genève 1991, D. F. Coray and Y.-F. S. Pétermann (eds.), Astérisque 209 (1992), 17-38.
  • [17] K. Győry, Bounds for the solutions of decomposable form equations, to appear.
  • [18] L. Hajdu, A quantitative version of Dirichlet's S-unit theorem in algebraic number fields, Publ. Math. Debrecen 42 (1993), 239-246.
  • [19] S. V. Kotov und L. A. Trelina, S-ganze Punkte auf elliptischen Kurven, J. Reine Angew. Math. 306 (1979), 28-41.
  • [20] S. Lang, Fundamentals of Diophantine Geometry, Springer, Berlin, 1983.
  • [21] H. W. Lenstra, Jr., Algorithms in algebraic number theory, Bull. Amer. Math. Soc. 26 (1992), 211-244.
  • [22] A. Pethő, Beiträge zur Theorie der S-Ordnungen, Acta Math. Acad. Sci. Hungar. 37 (1981), 51-57.
  • [23] W. M. Schmidt, Integer points on curves of genus 1, Compositio Math. 81 (1992), 33-59.
  • [24] T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge University Press, Cambridge, 1986.
  • [25] V. G. Sprindžuk, Classical Diophantine Equations, Lecture Notes in Math. 1559, Springer, 1993.
  • [26] M. Waldschmidt, Minorations de combinaisons linéaires de logarithmes de nombres algébriques, Canad. J. Math. 45 (1993), 176-224.
  • [27] K. Yu, Linear forms in p-adic logarithms III, Compositio Math. 91 (1994), 241-276
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav74i1p67bwm
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