Effective solution of families of Thue equations containing several parameters

 Access to full text

 Full (PDF)

1. [1] A. Baker and G. Wüstholz, Logarithmic forms and group varieties, J. Reine Angew. Math. 442 (1993), 19-62. Zbl0788.11026
2. [2] Yu. Bilu and G. Hanrot, Solving Thue equations of high degree, J. Number Theory 60 (1996), 373-392. Zbl0867.11017
3. [3] Y. Bugeaud and K. Győry, Bounds for the solutions of Thue-Mahler equations and norm form equations, Acta Arith. 74 (1996), 273-292. Zbl0861.11024
4. [4] J. H. Chen and P. M. Voutier, Complete solution of the Diophantine equation $X^2+1=d{Y}^4$ and a related family of quartic Thue equations, J. Number Theory 62 (1997), 71-99. Zbl0869.11025
5. [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. Zbl0733.11054
6. [6] I. Gaál and G. Lettl, A parametric family of quintic Thue equations, Math. Comp., to appear. Zbl0983.11014
7. [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. Zbl0965.11009
8. [8] C. Heuberger, On families of parametrized Thue equations, J. Number Theory 76 (1999), 45-61. 
9. [9] C. Heuberger, On a family of quintic Thue equations, J. Symbolic Comput. 26 (1998), 173-185. Zbl0915.11017
10. [10] C. Heuberger, A. Pethő and R. F. Tichy, Complete solution of parametrized Thue equations, Acta Math. Inform. Univ. Ostraviensis 6 (1998), 93-113. Zbl1024.11017
11. [11] S. Lang, Elliptic Curves: Diophantine Analysis, Grundlehren Math. Wiss. 23, Springer, Berlin, 1978. 
12. [12] E. Lee, Studies on Diophantine equations, Ph.D. thesis, Cambridge Univ., 1992. 
13. [13] G. Lettl and A. Pethő, Complete solution of a family of quartic Thue equations, Abh. Math. Sem. Univ. Hamburg 65 (1995), 365-383. Zbl0853.11021
14. [14] G. Lettl, A. Pethő and P. Voutier, Simple families of Thue inequalities, Trans. Amer. Math. Soc. 351 (1999), 1871-1894. Zbl0920.11041
15. [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. Zbl0923.11053
16. [16] M. Mignotte, Verification of a conjecture of E. Thomas, J. Number Theory 44 (1993), 172-177. 
17. [17] M. Mignotte, A. Pethő and F. Lemmermeyer, On the family of Thue equations $x^3-(n-1)x^{2}y-(n+2)x{y}^2-y^3=k$, Acta Arith. 76 (1996), 245-269. Zbl0862.11028
18. [18] M. Mignotte, A. Pethő and R. Roth, Complete solutions of quartic Thue and index form equations, Math. Comp. 65 (1996), 341-354. Zbl0853.11022
19. [19] M. Mignotte and N. Tzanakis, On a family of cubics, J. Number Theory 39 (1991), 41-49. 
20. [20] A. Pethő, Complete solutions to families of quartic Thue equations, Math. Comp. 57 (1991), 777-798. Zbl0738.11028
21. [21] A. Pethő and R. F. Tichy, On two-parametric quartic families of Diophantine problems, J. Symbolic Comput. 26 (1998), 151-171. Zbl0926.11016
22. [22] M. Pohst, Regulatorabschätzungen für total reelle algebraische Zahlkörper, J. Number Theory 9 (1977), 459-492. Zbl0366.12011
23. [23] M. Pohst and H. Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge Univ. Press, Cambridge, 1989. 
24. [24] I. Schur, Aufgabe 226, Arch. Math. Physik 13 (1908), 367. 
25. [25] E. Thomas, Complete solutions to a family of cubic Diophantine equations, J. Number Theory 34 (1990), 235-250. Zbl0697.10011
26. [26] E. Thomas, Solutions to certain families of Thue equations, ibid. 43 (1993), 319-369. Zbl0774.11013
27. [27] A. Thue, Über Annäherungswerte algebraischer Zahlen, J. Reine Angew. Math. 135 (1909), 284-305. 
28. [28] I. Wakabayashi, On a family of quartic Thue inequalities I, J. Number Theory 66 (1997), 70-84. Zbl0884.11021
29. [29] M. Waldschmidt, Minoration de combinaisons linéaires de logarithmes de nombres algébriques, Canad. J. Math. 45 (1993), 176-224.