How to explicitly solve a Thue-Mahler equation
Compositio Mathematica, Tome 84 (1992) no. 3, pp. 223-288.
corrigé par Corrections to “How to explicitly solve a Thue-Mahler equation” 
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     title = {How to explicitly solve a {Thue-Mahler} equation},
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Tzanakis, N.; de Weger, B. M. M. How to explicitly solve a Thue-Mahler equation. Compositio Mathematica, Tome 84 (1992) no. 3, pp. 223-288. http://archive.numdam.org/item/CM_1992__84_3_223_0/

[ACHP] A K. Agrawal, J. Coates, D. C. Hunt and A.J. Van Der Poorten, Elliptic curves of conductor 11, Math. Comput. 35 (1980), 991-1002. | MR | Zbl

[Be] W.E.H. Berwick, Algebraic number-fields with two independent units, Proc. London Math. Soc. 34 (1932), 360-378. | Zbl

[BGMMS] J. Blass, A.M.W. Glass, D.K. Manski, D.B. Meronk and R.P. Steiner, Constants for lower bounds for linear forms in logarithms of algebraic numbers II. The homogeneous rational case, Acta Arith. 55 (1990), 15-22. | MR | Zbl

[Bi1] K.K. Billevič, On the units of algebraic fields of third and fourth degree (Russian), Mat. Sb. 40, 82 (1956), 123-137. | MR | Zbl

[Bi2] K.K. Billevič, A theorem on the units of algebraic fields of nth degree, (Russian), Mat. Sb. 64, 106 (1964), 145-152. | MR

[BS] Z.I. Borevich and I.R. Shafarevich, Number theory, Academic Press, New York, London, 1973. | Zbl

[Bu1] J. Buchmann, The generalized Voronoi algorithm in totally real algebraic number fields, Eurocal '85, Linz 1985, Vol. 2, Lecture Notes in Comput. Sci. 204, Springer, Berlin, New York, 1985, pp. 479-486. | MR | Zbl

[Bu2] J. Buchmann, A generalization of Voronoi's unit algorithm I, J. Number Th. 20 (1986), 177-191. | MR | Zbl

[Bu3] J. Buchmann, A generalization of Voronoi's unit algorithm II, J. Number Th. 20 (1986), 192-209. | MR | Zbl

[Bu4] J. Buchmann, On the computation of units and class numbers by a generalization of Lagrange's algorithm, J. Number Th. 26 (1987), 8-30. | MR | Zbl

[Bu5] J. Buchmann, The computation of the fundamental unit of totally complex quartic orders, Math. Comput. 48 (1987), 39-54. | MR | Zbl

[DF] B.N. Delone and D.K. Faddeev, The theory of irrationalities of the third degree, Vol. 10, Transl. of Math. Monographs, Am. Math. Soc, Rhode Island, 1964. | MR | Zbl

[Ev] J.-H. Evertse, On equations in S-units and the Thue-Mahler equation, Invent. Math. 75 (1984), 561-584. | MR | Zbl

[FP] U. Fincke and M. Pohst, Improved methods for calculating vectors of short length in a lattice, including a complexity analysis, Math. Comput. 44 (1985), 463-471. | MR | Zbl

[Ko] N. Koblitz, p-adic numbers, p-adic analysis, and zeta-functions, Springer Verlag, New York, 1977. | MR | Zbl

[LLL] A K. Lenstra, H. W. Lenstra Jr. and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261 (1983), 515-534. | MR | Zbl

[Ma] K. Mahler, Zur Approximation algebraischer Zahlen, I: Über den grössten Primteiler binärer Formen, Math. Ann. 107 (1933), 691-730. | JFM | MR | Zbl

[Na1] W. Narkiewicz, Elementary and analytic theory of algebraic numbers, Polish Scientific Publishers, Warszawa, 1974. | MR | Zbl

[Na2] W. Narkiewicz, Elementary and analytic theory of algebraic numbers, 2nd ed., Polish Scientific Publishers, Warszawa, 1990. | MR | Zbl

[PW] A. Pethö and B.M.M. De Weger, Products of prime powers in binary recurrence sequences I. The hyperbolic case, with an application to the generalized Ramanujan-Nagell equation, Math. Comput. 47 (1986), 713-727. | MR | Zbl

[PZ1] M. Pohst and H. Zassenhaus, On effective computation of fundamental units I, Math. Comput. 38 (1982), 275-291. | MR | Zbl

[PZ2] M. Pohst, P. Weiler and H. Zassenhaus, On effective computation of fundamental units II, Math. Comput. 38 (1982), 293-329. | MR | Zbl

[PZ3] M. Pohst and H. Zassenhaus, Algorithmic algebraic number theory, Cambridge University Press, Cambridge, 1989. | MR | Zbl

[Sm] J. Graf Von Schmettow, KANT - a tool for computations in algebraic number fields, A. Pethö, M. Pohst, H. C. Williams and H. G. Zimmer, eds., Computational Number Theory, Walter de Gruyter & Co., Berlin, 1991, pp. 321-330. | MR | Zbl

[Sp] V.G. Sprindžuk, Classical diophantine equations in two unknowns (Russian), Nauka, Moskva, 1982. | MR | Zbl

[ST] T.N. Shorey and R. Tijdeman, Exponential diophantine equations, Cambridge University Press, Cambridge, 1986. | MR | Zbl

[Th] A. Thue, Über Annäherungswerten algebraischer Zahlen, J. reine angew. Math. 135 (1909), 284-305. | JFM

[TW1] N. Tzanakis and B.M.M. De Weger, On the practical solution of the Thue equation, J. Number Th. 31 (1989), 99-132. | MR | Zbl

[TW2] N. Tzanakis and B.M.M. De Weger, Solving a specific Thue-Mahler equation, Math. Comput. 57 (No. 196) (1991), 799-815. | MR | Zbl

[TW3] N. Tzanakis and B.M.M. Deweger, "On the practical solution of the Thue-Mahler equation, A. Pethö, M. Pohst, H. C. Williams and H. G. Zimmer, eds., Computational Number Theory, Walter de Gruyter & Co., Berlin, 1991, pp. 289-294. | MR | Zbl

[Wa] M. Waldschmidt, A lower bound for linear forms in logarithms, Acta Arith. 37 (1980), 257-283. | MR | Zbl

[dW1] B.M.M. De Weger, Algorithms for diophantine equations, CWI-Tract No. 65, Centre for Math. and Comp. Sci., Amsterdam, 1989. | MR | Zbl

[dW2] B.M.M. De Weger, On the practical solution of Thue-Mahler equations, an outline, K. Györy and G. Halász, eds., Number Theory, Coll. Math. Soc. János Bolyai, Vol. 51, Budapest, 1990, pp. 1037-1050. | MR | Zbl

[Yu1] Kunrui Yu, Linear forms in p-adic logarithms, Acta Arith. 53 (1989), 107-186. | MR | Zbl

[Yu2] Kunrui Yu, Linear forms in p-adic logarithms II, Compositio Math. 74 (1990), 15-113. | Numdam | MR | Zbl