Some diophantine equations of the form $x^n + y^n = z^m$

• Autorzy: Bjorn Poonen
• Języki publikacji: EN

Słowa kluczowe

EN

generalized Fermat equation; diophantine equations; descent

Kategorie tematyczne

• 11D41: Higher degree equations; Fermat's equation
• 11G30: Curves of arbitrary genus or genus ≠ 1 over global fields
• 11G05: Elliptic curves over global fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 86
• Numer: 3
• Strony: 193-205

Daty

wydano

1998

otrzymano

1997-03-04

Twórcy

autor

Bjorn Poonen

• Department of Mathematics, University of California, Berkeley, California 94720-3840, U.S.A.

Bibliografia

• [Be] F. Beukers, The Diophantine equation $Ax^p + By^q = Cz^r$, Duke Math. J. 91 (1998), no. 1, 61-88.
• [Ca] J. W. S. Cassels, The Mordell-Weil group of curves of genus 2, in: Arithmetic and Geometry, Vol. I, Progr. Math. 35, Birkhäuser, Boston, Mass., 1983, 27-60.
• [Cr] J. E. Cremona, Algorithms for Modular Elliptic Curves, Cambridge Univ. Press, 1992.
• [DM] H. Darmon and L. Merel, Winding quotients and some variants of Fermat's Last Theorem, J. Reine Angew. Math. 490 (1997), 81-100.
• [De] P. Dénes, Über die Diophantische Gleichung $x^l + y^l =cz^l$, Acta Math. 88 (1952), 241-251.
• [PS] B. Poonen and E. F. Schaefer, Explicit descent for Jacobians of cyclic covers of the projective line, J. Reine Angew. Math. 488 (1997), 141-188.
• [Sc] E. F. Schaefer, Computing a Selmer group of a Jacobian using functions on the curve, Math. Ann. 310 (1998), 447-471.