Duke Mathematical Journal

The Diophantine equation Axp+Byq=Czr

Frits Beukers

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J., Volume 91, Number 1 (1998), 61-88.

Dates
First available in Project Euclid: 19 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077231890

Digital Object Identifier
doi:10.1215/S0012-7094-98-09105-0

Mathematical Reviews number (MathSciNet)
MR1487980

Zentralblatt MATH identifier
1038.11505

Subjects
Primary: 11D41: Higher degree equations; Fermat's equation
Secondary: 20H10: Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]

Citation

Beukers, Frits. The Diophantine equation $Ax^p+By^q=Cz^r$. Duke Math. J. 91 (1998), no. 1, 61--88. doi:10.1215/S0012-7094-98-09105-0. https://projecteuclid.org/euclid.dmj/1077231890


Export citation

References

  • [DG] H. Darmon and A. Granville, On the equations $z\sp m=F(x,y)$ and $Ax\sp p+By\sp q=Cz\sp r$, Bull. London Math. Soc. 27 (1995), no. 6, 513–543.
  • [DM] H. Darmon and L. Merel, Winding quotients and some variants of Fermat's last theorem, to appear in J. Reine Angew. Math.
  • [FL] W. Fulton and R. Lazarsfeld, Connectivity and its applications in algebraic geometry, Algebraic geometry (Chicago, Ill., 1980), Lecture Notes in Math., vol. 862, Springer, Berlin, 1981, pp. 26–92.
  • [Mo] L. J. Mordell, Diophantine Equations, Pure and Applied Mathematics, vol. 30, Academic Press, London, 1969.
  • [S] J.-P. Serre, Local fields, Graduate Texts in Mathematics, vol. 67, Springer-Verlag, New York, 1979.
  • [ST] G. C. Shephard and J. A. Todd, Finite unitary reflection groups, Canadian J. Math. 6 (1954), 274–304.
  • [Sp1] T. A. Springer, Invariant theory, Lecture Notes in Math., Springer-Verlag, Berlin, 1977.
  • [Sp2] T. A. Springer, Regular elements of finite reflection groups, Invent. Math. 25 (1974), 159–198.
  • [T] S. Thiboutot, Courbes elliptiques, représentations galoisiennes et l'équation $x^2+y^3=z^5$, McGill Univ., Montreal, 1996.
  • [W] W. C. Waterhouse, Introduction to affine group schemes, Graduate Texts in Mathematics, vol. 66, Springer-Verlag, New York, 1979.