Effective solution of families of Thue equations containing several parameters
Clemens Heuberger ; Robert F. Tichy
Acta Arithmetica, Tome 89 (1999), p. 147-163 / Harvested from The Polish Digital Mathematics Library
Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:207345
@article{bwmeta1.element.bwnjournal-article-aav91i2p147bwm,
     author = {Clemens Heuberger and Robert F. Tichy},
     title = {Effective solution of families of Thue equations containing several parameters},
     journal = {Acta Arithmetica},
     volume = {89},
     year = {1999},
     pages = {147-163},
     zbl = {0944.11008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav91i2p147bwm}
}
Clemens Heuberger; Robert F. Tichy. Effective solution of families of Thue equations containing several parameters. Acta Arithmetica, Tome 89 (1999) pp. 147-163. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav91i2p147bwm/

[000] [1] A. Baker and G. Wüstholz, Logarithmic forms and group varieties, J. Reine Angew. Math. 442 (1993), 19-62. | Zbl 0788.11026

[001] [2] Yu. Bilu and G. Hanrot, Solving Thue equations of high degree, J. Number Theory 60 (1996), 373-392. | Zbl 0867.11017

[002] [3] Y. Bugeaud and K. Győry, Bounds for the solutions of Thue-Mahler equations and norm form equations, Acta Arith. 74 (1996), 273-292. | Zbl 0861.11024

[003] [4] J. H. Chen and P. M. Voutier, Complete solution of the Diophantine equation X2+1=dY4 and a related family of quartic Thue equations, J. Number Theory 62 (1997), 71-99. | Zbl 0869.11025

[004] [5] I. Gaál, On the resolution of some Diophantine equations, in: Computational Number Theory, A. Pethő, M. Pohst, H. C. Williams and H. G. Zimmer (eds.), de Gruyter, Berlin, 1991, 261-280. | Zbl 0733.11054

[005] [6] I. Gaál and G. Lettl, A parametric family of quintic Thue equations, Math. Comp., to appear. | Zbl 0983.11014

[006] [7] F. Halter-Koch, G. Lettl, A. Pethő and R. F. Tichy, Thue equations associated with Ankeny-Brauer-Chowla number fields, J. London Math. Soc., to appear. | Zbl 0965.11009

[007] [8] C. Heuberger, On families of parametrized Thue equations, J. Number Theory 76 (1999), 45-61.

[008] [9] C. Heuberger, On a family of quintic Thue equations, J. Symbolic Comput. 26 (1998), 173-185. | Zbl 0915.11017

[009] [10] C. Heuberger, A. Pethő and R. F. Tichy, Complete solution of parametrized Thue equations, Acta Math. Inform. Univ. Ostraviensis 6 (1998), 93-113. | Zbl 1024.11017

[010] [11] S. Lang, Elliptic Curves: Diophantine Analysis, Grundlehren Math. Wiss. 23, Springer, Berlin, 1978.

[011] [12] E. Lee, Studies on Diophantine equations, Ph.D. thesis, Cambridge Univ., 1992.

[012] [13] G. Lettl and A. Pethő, Complete solution of a family of quartic Thue equations, Abh. Math. Sem. Univ. Hamburg 65 (1995), 365-383. | Zbl 0853.11021

[013] [14] G. Lettl, A. Pethő and P. Voutier, Simple families of Thue inequalities, Trans. Amer. Math. Soc. 351 (1999), 1871-1894. | Zbl 0920.11041

[014] [15] G. Lettl, A. Pethő and P. Voutier, On the arithmetic of simplest sextic fields and related Thue equations, in: Number Theory, Diophantine, Computational and Algebraic Aspects (Eger, 1996), K. Győry, A. Pethő and V. T. Sós (eds.), de Gruyter, Berlin, 1998, 331-348. | Zbl 0923.11053

[015] [16] M. Mignotte, Verification of a conjecture of E. Thomas, J. Number Theory 44 (1993), 172-177.

[016] [17] M. Mignotte, A. Pethő and F. Lemmermeyer, On the family of Thue equations x3-(n-1)x2y-(n+2)xy2-y3=k, Acta Arith. 76 (1996), 245-269. | Zbl 0862.11028

[017] [18] M. Mignotte, A. Pethő and R. Roth, Complete solutions of quartic Thue and index form equations, Math. Comp. 65 (1996), 341-354. | Zbl 0853.11022

[018] [19] M. Mignotte and N. Tzanakis, On a family of cubics, J. Number Theory 39 (1991), 41-49.

[019] [20] A. Pethő, Complete solutions to families of quartic Thue equations, Math. Comp. 57 (1991), 777-798. | Zbl 0738.11028

[020] [21] A. Pethő and R. F. Tichy, On two-parametric quartic families of Diophantine problems, J. Symbolic Comput. 26 (1998), 151-171. | Zbl 0926.11016

[021] [22] M. Pohst, Regulatorabschätzungen für total reelle algebraische Zahlkörper, J. Number Theory 9 (1977), 459-492. | Zbl 0366.12011

[022] [23] M. Pohst and H. Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge Univ. Press, Cambridge, 1989.

[023] [24] I. Schur, Aufgabe 226, Arch. Math. Physik 13 (1908), 367.

[024] [25] E. Thomas, Complete solutions to a family of cubic Diophantine equations, J. Number Theory 34 (1990), 235-250. | Zbl 0697.10011

[025] [26] E. Thomas, Solutions to certain families of Thue equations, ibid. 43 (1993), 319-369. | Zbl 0774.11013

[026] [27] A. Thue, Über Annäherungswerte algebraischer Zahlen, J. Reine Angew. Math. 135 (1909), 284-305.

[027] [28] I. Wakabayashi, On a family of quartic Thue inequalities I, J. Number Theory 66 (1997), 70-84. | Zbl 0884.11021

[028] [29] M. Waldschmidt, Minoration de combinaisons linéaires de logarithmes de nombres algébriques, Canad. J. Math. 45 (1993), 176-224.