How to explicitly solve a Thue-Mahler equation
N. Tzanakis; B. M. M. de Weger
Compositio Mathematica (1992)
- Volume: 84, Issue: 3, page 223-288
- ISSN: 0010-437X
Access Full Article
topHow to cite
topTzanakis, N., and de Weger, B. M. M.. "How to explicitly solve a Thue-Mahler equation." Compositio Mathematica 84.3 (1992): 223-288. <http://eudml.org/doc/90185>.
@article{Tzanakis1992,
author = {Tzanakis, N., de Weger, B. M. M.},
journal = {Compositio Mathematica},
keywords = {algorithm; Thue-Mahler equation},
language = {eng},
number = {3},
pages = {223-288},
publisher = {Kluwer Academic Publishers},
title = {How to explicitly solve a Thue-Mahler equation},
url = {http://eudml.org/doc/90185},
volume = {84},
year = {1992},
}
TY - JOUR
AU - Tzanakis, N.
AU - de Weger, B. M. M.
TI - How to explicitly solve a Thue-Mahler equation
JO - Compositio Mathematica
PY - 1992
PB - Kluwer Academic Publishers
VL - 84
IS - 3
SP - 223
EP - 288
LA - eng
KW - algorithm; Thue-Mahler equation
UR - http://eudml.org/doc/90185
ER -
References
top- [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. Zbl0475.14031MR572871
- [Be] W.E.H. Berwick, Algebraic number-fields with two independent units, Proc. London Math. Soc.34 (1932), 360-378. Zbl0005.34203
- [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. Zbl0709.11037MR1056111
- [Bi1] K.K. Billevič, On the units of algebraic fields of third and fourth degree (Russian), Mat. Sb.40, 82 (1956), 123-137. Zbl0078.02901MR88516
- [Bi2] K.K. Billevič, A theorem on the units of algebraic fields of nth degree, (Russian), Mat. Sb.64, 106 (1964), 145-152. MR163902
- [BS] Z.I. Borevich and I.R. Shafarevich, Number theory, Academic Press, New York, London, 1973. Zbl0145.04902
- [Bu1] J. Buchmann, The generalized Voronoi algorithm in totally real algebraic number fields, Eurocal '85, Linz1985, Vol. 2, Lecture Notes in Comput. Sci.204, Springer, Berlin, New York, 1985, pp. 479-486. Zbl0586.12004MR826578
- [Bu2] J. Buchmann, A generalization of Voronoi's unit algorithm I, J. Number Th.20 (1986), 177-191. Zbl0575.12005MR790781
- [Bu3] J. Buchmann, A generalization of Voronoi's unit algorithm II, J. Number Th.20 (1986), 192-209. Zbl0575.12005MR790782
- [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. Zbl0615.12001MR883530
- [Bu5] J. Buchmann, The computation of the fundamental unit of totally complex quartic orders, Math. Comput.48 (1987), 39-54. Zbl0627.12004MR866097
- [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. Zbl0133.30202MR160744
- [Ev] J.-H. Evertse, On equations in S-units and the Thue-Mahler equation, Invent. Math.75 (1984), 561-584. Zbl0521.10015MR735341
- [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. Zbl0556.10022MR777278
- [Ko] N. Koblitz, p-adic numbers, p-adic analysis, and zeta-functions, Springer Verlag, New York, 1977. Zbl0364.12015MR466081
- [LLL] A K. Lenstra, H. W. Lenstra jr. and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann.261 (1983), 515-534. Zbl0488.12001MR682664
- [Ma] K. Mahler, Zur Approximation algebraischer Zahlen, I: Über den grössten Primteiler binärer Formen, Math. Ann.107 (1933), 691-730. Zbl0006.10502MR1512822JFM59.0220.01
- [Na1] W. Narkiewicz, Elementary and analytic theory of algebraic numbers, Polish Scientific Publishers, Warszawa, 1974. Zbl0276.12002MR347767
- [Na2] W. Narkiewicz, Elementary and analytic theory of algebraic numbers, 2nd ed., Polish Scientific Publishers, Warszawa, 1990. Zbl0717.11045MR1055830
- [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. Zbl0623.10011MR856715
- [PZ1] M. Pohst and H. Zassenhaus, On effective computation of fundamental units I, Math. Comput.38 (1982), 275-291. Zbl0493.12004MR637307
- [PZ2] M. Pohst, P. Weiler and H. Zassenhaus, On effective computation of fundamental units II, Math. Comput.38 (1982), 293-329. Zbl0493.12005MR637308
- [PZ3] M. Pohst and H. Zassenhaus, Algorithmic algebraic number theory, Cambridge University Press, Cambridge, 1989. Zbl0685.12001MR1033013
- [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. Zbl0731.11070MR1151875
- [Sp] V.G. Sprindžuk, Classical diophantine equations in two unknowns (Russian), Nauka, Moskva, 1982. Zbl0523.10008MR685430
- [ST] T.N. Shorey and R. Tijdeman, Exponential diophantine equations, Cambridge University Press, Cambridge, 1986. Zbl0606.10011MR891406
- [Th] A. Thue, Über Annäherungswerten algebraischer Zahlen, J. reine angew. Math.135 (1909), 284-305. JFM40.0265.01
- [TW1] N. Tzanakis and B.M.M. de Weger, On the practical solution of the Thue equation, J. Number Th.31 (1989), 99-132. Zbl0657.10014MR987566
- [TW2] N. Tzanakis and B.M.M. de Weger, Solving a specific Thue-Mahler equation, Math. Comput.57 (No. 196) (1991), 799-815. Zbl0738.11029MR1094961
- [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. Zbl0738.11030MR1151871
- [Wa] M. Waldschmidt, A lower bound for linear forms in logarithms, Acta Arith.37 (1980), 257-283. Zbl0357.10017MR598881
- [dW1] B.M.M. de Weger, Algorithms for diophantine equations, CWI-Tract No. 65, Centre for Math. and Comp. Sci., Amsterdam, 1989. Zbl0687.10013MR1026936
- [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. Zbl0703.11014MR1058259
- [Yu1] Kunrui Yu, Linear forms in p-adic logarithms, Acta Arith.53 (1989), 107-186. Zbl0699.10050MR1027200
- [Yu2] Kunrui Yu, Linear forms in p-adic logarithms II, Compositio Math.74 (1990), 15-113. Zbl0723.11034MR1055245
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.