@article{CM_1992__84_3_223_0,
author = {Tzanakis, N. and de Weger, B. M. M.},
title = {How to explicitly solve a {Thue-Mahler} equation},
journal = {Compositio Mathematica},
pages = {223--288},
year = {1992},
publisher = {Kluwer Academic Publishers},
volume = {84},
number = {3},
mrnumber = {1189890},
zbl = {0773.11023},
language = {en},
url = {https://www.numdam.org/item/CM_1992__84_3_223_0/}
}
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. https://www.numdam.org/item/CM_1992__84_3_223_0/
[ACHP] and , Elliptic curves of conductor 11, Math. Comput. 35 (1980), 991-1002. | Zbl | MR
[Be] , Algebraic number-fields with two independent units, Proc. London Math. Soc. 34 (1932), 360-378. | Zbl
[BGMMS] , , , and , Constants for lower bounds for linear forms in logarithms of algebraic numbers II. The homogeneous rational case, Acta Arith. 55 (1990), 15-22. | Zbl | MR
[Bi1] , On the units of algebraic fields of third and fourth degree (Russian), Mat. Sb. 40, 82 (1956), 123-137. | Zbl | MR
[Bi2] , A theorem on the units of algebraic fields of nth degree, (Russian), Mat. Sb. 64, 106 (1964), 145-152. | MR
[BS] and , Number theory, Academic Press, New York, London, 1973. | Zbl
[Bu1] , 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. | Zbl | MR
[Bu2] , A generalization of Voronoi's unit algorithm I, J. Number Th. 20 (1986), 177-191. | Zbl | MR
[Bu3] , A generalization of Voronoi's unit algorithm II, J. Number Th. 20 (1986), 192-209. | Zbl | MR
[Bu4] , On the computation of units and class numbers by a generalization of Lagrange's algorithm, J. Number Th. 26 (1987), 8-30. | Zbl | MR
[Bu5] , The computation of the fundamental unit of totally complex quartic orders, Math. Comput. 48 (1987), 39-54. | Zbl | MR
[DF] and , The theory of irrationalities of the third degree, Vol. 10, Transl. of Math. Monographs, Am. Math. Soc, Rhode Island, 1964. | Zbl | MR
[Ev] , On equations in S-units and the Thue-Mahler equation, Invent. Math. 75 (1984), 561-584. | Zbl | MR
[FP] and , Improved methods for calculating vectors of short length in a lattice, including a complexity analysis, Math. Comput. 44 (1985), 463-471. | Zbl | MR
[Ko] , p-adic numbers, p-adic analysis, and zeta-functions, Springer Verlag, New York, 1977. | Zbl | MR
[LLL] and , Factoring polynomials with rational coefficients, Math. Ann. 261 (1983), 515-534. | Zbl | MR
[Ma] , Zur Approximation algebraischer Zahlen, I: Über den grössten Primteiler binärer Formen, Math. Ann. 107 (1933), 691-730. | Zbl | MR | JFM
[Na1] , Elementary and analytic theory of algebraic numbers, Polish Scientific Publishers, Warszawa, 1974. | Zbl | MR
[Na2] , Elementary and analytic theory of algebraic numbers, 2nd ed., Polish Scientific Publishers, Warszawa, 1990. | Zbl | MR
[PW] and , 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. | Zbl | MR
[PZ1] and , On effective computation of fundamental units I, Math. Comput. 38 (1982), 275-291. | Zbl | MR
[PZ2] , and , On effective computation of fundamental units II, Math. Comput. 38 (1982), 293-329. | Zbl | MR
[PZ3] and , Algorithmic algebraic number theory, Cambridge University Press, Cambridge, 1989. | Zbl | MR
[Sm] , 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. | Zbl | MR
[Sp] , Classical diophantine equations in two unknowns (Russian), Nauka, Moskva, 1982. | Zbl | MR
[ST] and , Exponential diophantine equations, Cambridge University Press, Cambridge, 1986. | Zbl | MR
[Th] , Über Annäherungswerten algebraischer Zahlen, J. reine angew. Math. 135 (1909), 284-305. | JFM
[TW1] and , On the practical solution of the Thue equation, J. Number Th. 31 (1989), 99-132. | Zbl | MR
[TW2] and , Solving a specific Thue-Mahler equation, Math. Comput. 57 (No. 196) (1991), 799-815. | Zbl | MR
[TW3] and , "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. | Zbl | MR
[Wa] , A lower bound for linear forms in logarithms, Acta Arith. 37 (1980), 257-283. | Zbl | MR
[dW1] , Algorithms for diophantine equations, CWI-Tract No. 65, Centre for Math. and Comp. Sci., Amsterdam, 1989. | Zbl | MR
[dW2] , 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. | Zbl | MR
[Yu1] , Linear forms in p-adic logarithms, Acta Arith. 53 (1989), 107-186. | Zbl | MR
[Yu2] , Linear forms in p-adic logarithms II, Compositio Math. 74 (1990), 15-113. | Zbl | MR | Numdam





