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

Acta Arithmetica

Volumn 74, Issue 3, 1996, Pages 273-292

  Bugeaud, Yann ^a   Györy, Kálmán ^b  

^a UNIVERSITÉ DE STRASBOURG   (France)

^b UNIVERSITY OF DEBRECEN   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030449306     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa-74-3-273-292     Document Type: Article

References (25)

1. A. Baker, Transcendental Number Theory, 2nd ed., Cambridge University Press, 1979.
2. m, Ann. Scuola Norm. Sup. Pisa (IV) 20 (1993), 61-89.
3. Y. Bugeaud and K. Györy, Bounds for the solutions of unit equations, Acta Arith. 74 (1996), 67-80.
4. J. H. Evertse and K. Györy, Decomposable form equations, in: New Advances in Transcendence Theory, A. Baker (ed.), Cambridge University Press, 1988, 175-202.
5. J. H. Evertse, K. Györy, 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. Györy, Sur les polynômes à coefficients entiers et de discriminant donné II, Publ. Math. Debrecen 21 (1974), 125-144.
9. _, Explicit upper bounds for the solutions of some diophantine equations, Ann. Acad. Sci. Fenn. Ser. A Math. 5 (1980), 3-12.
10. _, Explicit lower bounds for linear forms with algebraic coefficients, Arch. Math. (Basel) 35 (1980), 438-446.
11. _, 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. _, On the representation of integers by decomposable forms in several variables, Publ. Math. Debrecen 28 (1981), 89-98.
13. _, On S-integral solutions of norm form, discriminant form and index form equations, Studia Sci. Math. Hungar. 16 (1981), 149-161.
14. K. Györy 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. Sprindzuk, 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.