This is a preview of subscription content, log in via an institution to check access.
References
Beukers, F.: The generalised Ramanujan-Nagell equation. Thesis, Leiden 1979
Beukers, F.: On the generalized Ramanujan-Nagell equation. I. Acta Arith.38, 389–410 (1980/81)
Beukers, F.: On the generalized Ramanujan-Nagell equation. II. Acta Arith.39, 113–123 (1981)
Choodnovsky, G.V.: The Gel'fond-Baker method in problems of diophantine approximation. Coll. Math. Soc. János Bolyai13, 19–30 (1974)
Delone, B.N.: Über die Darstellung der Zahlen durch die binären kubischen Formen von negativer Diskriminante. Math. Z.31, 1–26 (1930)
Evertse, J.H.: On the equationax n −by n=c. Compositio Math.47, 289–315 (1982)
Evertse, J.H.: On the representation of integers by binary cubic forms of positive discriminant. Invent. Math.73, 117–138 (1983)
Evertse, J.H.: Upper bounds for the numbers of solutions of diophantine equations. MC-tract, Mathematisch Centrum, Amsterdam 1983
Faltings, G.: Endlichkeitssätze für abelsche Varietäten über Zahlkörpern. Invent. Math.73, 349–366 (1983)
Györy, K.: On the number of solutions of linear equations in units of an algebraic number field. Comm. Math. Helv.54, 583–600 (1979)
Lewis, D.J., Mahler, K.: Representation of integers by binary forms. Acta Arith.6, 333–363 (1960/61)
Mahler, K.: Zur Approximation algebraischer Zahlen. I. Über den größten Primteiler binärer Formen. Math. Ann.107, 691–730 (1933)
Mahler, K.: Zur Approximation algebraischer Zahlen. II. Über die Anzahl der Darstellungen ganzer Zahlen durch Binärformen. Math. Ann.108, 37–55 (1933)
Mahler, K.: On Thue's theorem. Austral. Nat. Un. Math. Res. Rep.24, (1982); Math. Scand. in press (1984)
Mordell, L.J.: Diophantine equations. London: Academic Press 1969
Nagell, T.: Darstellung ganzer Zahlen durch binäre kubische Formen mit negativer Diskriminante. Math. Z.28, 10–29 (1928)
Nagell, T.: The diophantine equationx 2+7=2n, Norsk Mat. Tidsskr.30, 62–64 (1948); Ark. Mat.4, 185–187 (1960)
Parry, C.J.: Thep-adic generalisation of the Thue-Siegel theorem. Acta Math.83, 1–99 (1950)
Ramanujan, S.: Collected papers: p. 327. Chelsea Publ. Co., New York (1962)
Siegel, C.L.: Die Gleichungax n −by n=c. Math. Ann.114, 57–68 (1937); Gesammelte Abhandlungen, vol. 2. pp. 8–19. Berlin-Heidelberg-New York: Springer 1966
Silverman, J.H.: Integer points and the rank of Thue elliptic curves. Invent. Math.66, 395–404 (1982)
Silverman, J.H.: The Thue equation and height functions. In: Bertrand, D., Waldschmidt, M. eds. Approximations diophantienne et nombres transcendents. Coll. Luminy 1982, pp. 259–270. Boston-Basel-Stuttgart: Birkhäuser 1983
Silverman, J.H.: Quantitative results in diophantine geometry. Preprint, Massachusetts Inst. of Techn.
Tartakovskii, V.A.: A uniform estimate of the number of representations of unity by a binary form of degreen≧3. Dokl. Akad. Nauk. SSSR193: (1970) (Russian): Soviet Math. Dokl.11, 1026–1027 (1970)
Thue, A.: Berechnung aller Lösungen gewisser Gleichungen von der Formax r −by r=f, Vid. Selsk. Skrifter I. mat-naturv. Kl., Christiania 1918, Nr. 4; Selected Mathematical Papers of Axel Thue, pp. 565–572. Oslo, Bergen, Tromsø (1977)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Evertse, J.H. On equations inS-units and the Thue-Mahler equation. Invent Math 75, 561–584 (1984). https://doi.org/10.1007/BF01388644
Issue Date:
DOI: https://doi.org/10.1007/BF01388644