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1996 | 74 | 3 | 273-292
Tytuł artykułu

Bounds for the solutions of Thue-Mahler equations and norm form equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
74
Numer
3
Strony
273-292
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-07-10
Twórcy
autor
  • Université Louis Pasteur, 7, Rue René Descartes, 67084 Strasbourg, France
  • Institute of Mathematics, Kossuth Lajos University, 4010 Debrecen, Hungary
Bibliografia
  • [1] A. Baker, Transcendental Number Theory, 2nd ed., Cambridge University Press, 1979.
  • [2] E. Bombieri, Effective diophantine approximation on Gₘ, Ann. Scuola Norm. Sup. Pisa (IV) 20 (1993), 61-89.
  • [3] Y. Bugeaud and K. Győry, Bounds for the solutions of unit equations, Acta Arith. 74 (1996), 67-80.
  • [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] 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.
  • [6] N. I. Feldman, An effective refinement of the exponent in Liouville's theorem, Izv. Akad. Nauk SSSR 35 (1971), 973-990 (in Russian).
  • [7] I. Gaál, Norm form equations with several dominating variables and explicit lower bounds for inhomogeneous linear forms with algebraic coefficients II, Studia Sci. Math. Hungar. 20 (1985), 333-344.
  • [8] K. Győry, Sur les polynômes à coefficients entiers et de discriminant donné II, Publ. Math. Debrecen 21 (1974), 125-144.
  • [9] K. Győry, Explicit upper bounds for the solutions of some diophantine equations, Ann. Acad. Sci. Fenn. Ser. A Math. 5 (1980), 3-12.
  • [10] K. Győry, Explicit lower bounds for linear forms with algebraic coefficients, Arch. Math. (Basel) 35 (1980), 438-446.
  • [11] K. Győry, Résultats effectifs sur la représentation des entiers par des formes décomposables, Queen's Papers in Pure and Appl. Math. 56, Queen's University, Kingston, 1980.
  • [12] K. Győry, On the representation of integers by decomposable forms in several variables, Publ. Math. Debrecen 28 (1981), 89-98.
  • [13] K. Győry, On S-integral solutions of norm form, discriminant form and index form equations, Studia Sci. Math. Hungar. 16 (1981), 149-161.
  • [14] K. Győry and Z. Z. Papp, Norm form equations and explicit lower bounds for linear forms with algebraic coefficients, in: Studies in Pure Mathematics to the Memory of Paul Turán, Akadémiai Kiadó, Budapest, and Birkhäuser, Basel, 1983, 245-257.
  • [15] L. Hajdu, A quantitative version of Dirichlet's S-unit theorem in algebraic number fields, Publ. Math. Debrecen 42 (1993), 239-246.
  • [16] S. V. Kotov, Effective bound for a linear form with algebraic coefficients in the archimedean and p-adic metrics, Inst. Math. Akad. Nauk BSSR, Preprint No. 24, Minsk, 1981 (in Russian).
  • [17] S. V. Kotov and V. G. Sprindžuk, The Thue-Mahler equation in relative fields and approximation of algebraic numbers by algebraic numbers, Izv. Akad. Nauk SSSR 41 (1977), 723-751 (in Russian).
  • [18] H. W. Lenstra, Jr., Algorithms in algebraic number theory, Bull. Amer. Math. Soc. 26 (1992), 211-244.
  • [19] D. J. Lewis and K. Mahler, On the representation of integers by binary forms, Acta Arith. 6 (1961), 333-363.
  • [20] W. M. Schmidt, Integer points on curves of genus 1, Compositio Math. 81 (1992), 33-59.
  • [21] T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge University Press, Cambridge, 1986.
  • [22] V. G. Sprindžuk, Classical Diophantine Equations, Lecture Notes in Math. 1559, Springer, 1993.
  • [23] P. Voutier, An effective lower bound for the height of algebraic numbers, Acta Arith. 74 (1996), 81-95.
  • [24] M. Waldschmidt, Minorations de combinaisons linéaires de logarithmes de nombres algébriques, Canad. J. Math. 45 (1993), 176-224.
  • [25] 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-aav74i3p273bwm
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