| Title:
|
Complete solution of parametrized Thue equations (English) |
| Author:
|
Heuberger, C. |
| Author:
|
Pethő, A. |
| Author:
|
Tichy, R. F. |
| Language:
|
English |
| Journal:
|
Acta Mathematica et Informatica Universitatis Ostraviensis |
| ISSN:
|
1211-4774 |
| Volume:
|
6 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
93-114 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11D57 |
| MSC:
|
11D59 |
| MSC:
|
11Y50 |
| idZBL:
|
Zbl 1024.11017 |
| idMR:
|
MR1822519 |
| . |
| Date available:
|
2009-01-30T09:06:13Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/120521 |
| . |
| Reference:
|
[1] A. Baker. : Contribution to the theory of Diophantine equations I.On the representation of integers by binary forms. Philos. Trans. Roy. Soc. London Ser. A, 263:173-191, 1968. MR 0228424 |
| Reference:
|
[2] A. Baker, H. Davenport. : The equations $3x^2 - 2 = y^2$ and $8x^2 - 7 = z^2$.Quart. J. Math. Oxford, 20:129-137, 1969. MR 0248079 |
| Reference:
|
[3] A. Baker, G. Wüstholz. : Logarithmic forms and group varieties.J. reine angew. Math., 442:19-62, 1993. Zbl 0788.11026, MR 1234835 |
| Reference:
|
[4] Yu. Bilu, G. Hanrot. : Solving Thue Equations of High Degree.J. Number Theory, 60:373-392, 1996. Zbl 0867.11017, MR 1412969 |
| Reference:
|
[5] E. Bombieri, W. M. Schmidt. : On Thue's equation.Invent. Math., 88:69- 81, 1987. Zbl 0614.10018, MR 0877007, 10.1007/BF01405092 |
| Reference:
|
[6] Y. Bugeaud, K. Gyory. : Bounds for the solutions of Thue-Mahler equations and norm form equations.Acta Arith., 74(3):273-292, 1996. Zbl 0861.11024, MR 1373714 |
| Reference:
|
[7] J. H. Chen, P. M. Voutier. : Complete solution of the Diophantine Equation $X^2 + 1 = dY^4$ and a Related Family of Quartic Thue Equations.J. Number Theory, 62:71-99, 1997. MR 1430002 |
| Reference:
|
[8] H. Cohen. : A Course in Computational Algebraic Number Theory.volume 138 of Graduate Texts in Mathematics. Springer, Berlin etc., third edition, 1996. MR 1228206 |
| Reference:
|
[9] M. Daberkow C. Fieker J. Kluners M. E. Pohst K. Roegner, and K. Wildanger. : KANT V4.To appear in J. Symbolic Cornput., 1997. |
| Reference:
|
[10] I. Gaal. : On the resolution of some diophantine equations.In A. Petho, M. Pohst, H. C. Williams, and H. G. Zimmer, editors, Computational Number Theory, pages 261-280. De Gruyter, Berlin - New York, 1991. Zbl 0733.11054, MR 1151869 |
| Reference:
|
[11] F. Halter-Koch G. Lettl A. Petho, and R. F. Tichy. : Thue equations associated with Ankeny-Brauer-Chowla Number Fields.To appear in J. London Math. Soc. MR 1721811 |
| Reference:
|
[12] C. Heuberger. : On a family of quintic Thue equations.To appear in J. Symbolic Comput. Zbl 0915.11017, MR 1635238 |
| Reference:
|
[13] S. Lang. : Elliptic Curves: Diophantine Analysis.volume 23 of Grundlehren der Mathematischen Wissenschaften. Springer, Berlin - New York, 1978. Zbl 0388.10001, MR 0518817 |
| Reference:
|
[14] M. Laurent M. Mignotte, and Yu. Nesterenko. : Formes lineaires en deux logarithmes et determinants d'interpolation.J. Number Theory, 55:285-321, 1995. MR 1366574 |
| Reference:
|
[15] E. Lee. : Studies on Diophantine equations.PhD thesis, Cambridge University, 1992. |
| Reference:
|
[16] G. Lettl, A. Petho. : Complete Solution of a Family of Quartic Thue Equations.Abh. Math. Sem. Univ. Hamburg, 65:365-383, 1995. Zbl 0853.11021, MR 1359142 |
| Reference:
|
[17] G. Lettl A. Petho, and P. Voutier. : On the arithmetic of simplest sextic fields and related Thue equations.In K. Gyory, A. Petho, and V. T. Sos, editors, Number Theory, Diophantine, Computational and Algebraic Aspects, pages 331-348. W. de Gruyter Publ. Co, 1998. MR 1628852 |
| Reference:
|
[18] G. Lettl A. Petho, and P. Voutier. : Simple families of Thue inequalities.To appear in Trans. Amer. Math. Soc. MR 1487624 |
| Reference:
|
[19] K. Mahler. : An inequality for the discriminant of a polynomial.Michigan Math. J., 11:257-262, 1964. Zbl 0135.01702, MR 0166188 |
| Reference:
|
[20] M. Mignotte. : Pethö's cubics.Preprint. Zbl 0960.11020 |
| Reference:
|
[21] M. Mignotte. : Verification of a Conjecture of E. Thomas.J. Number Theory, 44:172-177, 1993. Zbl 0780.11013, MR 1225951 |
| Reference:
|
[22] M. Mignotte A. Pethö, and R. Roth. : Complete solutions of quartic Thue and index form equations.Math. Comp., 65:341-354, 1996. MR 1316596 |
| Reference:
|
[23] M. Mignotte A. Pethö, and F. Lemmermeyer. : On the family of Thue equations $x^3 - (n - 1)x{^2}y - (n + 2)xy^2 - y^3 = k$.Acta Arith., 76:245-269, 1996. MR 1397316 |
| Reference:
|
[24] M. Mignotte, N. Tzanakis. : On a family of cubics.J. Number Theory, 39:41-49, 1991. Zbl 0734.11025, MR 1123167 |
| Reference:
|
[25] A. Pethö. : Complete solutions to families of quartic Thue equations.Math. Comp., 57:777-798, 1991. Zbl 0738.11028, MR 1094956 |
| Reference:
|
[26] A. Pethö, R. Schulenberg. : Effektives Losen von Thue Gleichungen.Publ. Math. Debrecen, 34:189-196, 1987. MR 0934900 |
| Reference:
|
[27] A. Pethö, R. F. Tichy. : On two-parametric quartic families of diophantine problems.To appear in J. Symbolic Comput. MR 1635234 |
| Reference:
|
[28] M. Pohst, H. Zassenhaus. : Algorithmic algebraic number theory.Cambridge University Press, Cambridge etc., 1989. Zbl 0685.12001, MR 1033013 |
| Reference:
|
[29] E. Thomas. : Complete Solutions to a Family of Cubic Diophantine Equations.J. Number Theory, 34:235-250, 1990. Zbl 0697.10011, MR 1042497 |
| Reference:
|
[30] E. Thomas. : Solutions to Certain Families of Thue Equations.J. Number Theory, 43:319-369, 1993. Zbl 0774.11013, MR 1212687 |
| Reference:
|
[31] A. Thue. : Über Annaherungswerte algebraischer Zahlen.J. reine angew. Math., 135:284-305, 1909. |
| Reference:
|
[32] N. Tzanakis, B. M. M. de Weger. : On the practical solution of the Thue equation.J. Number Theory, 31:99-132, 1989. Zbl 0657.10014, MR 0987566 |
| Reference:
|
[33] P. Voutier. : Linear forms in three logarithms.Preprint. |
| Reference:
|
[34] I. Wakabayashi. : On a Family of Quartic Thue Inequalities I.J. Number Theory, 66:70-84, 1997. Zbl 0884.11021, MR 1467190 |
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