On the equation a³ + b³ⁿ = c²

• Autorzy: Michael A. Bennett , Imin Chen , Sander R. Dahmen , Soroosh Yazdani
• Języki publikacji: EN

Abstrakty

EN

We study coprime integer solutions to the equation a³ + b³ⁿ = c² using Galois representations and modular forms. This case represents perhaps the last natural family of generalized Fermat equations descended from spherical cases which is amenable to resolution using the so-called modular method. Our techniques involve an elaborate combination of ingredients, ranging from ℚ-curves and a delicate multi-Frey approach, to appeal to intricate image of inertia arguments.

Kategorie tematyczne

• 11D61: Exponential equations
• 11D41: Higher degree equations; Fermat's equation
• 14G05: Rational points
• 11G05: Elliptic curves over global fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 163
• Numer: 4
• Strony: 327-343

Daty

wydano

2014

Twórcy

autor

Michael A. Bennett

• Department of Mathematics, University of British Columbia, Vancouver, British Columbia, V6T 1Z2, Canada

autor

Imin Chen

• Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada

autor

Sander R. Dahmen

• Department of Mathematics, VU University Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands

autor

Soroosh Yazdani

• Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Alberta, T1K 3M4, Canada

Identyfikatory

DOI

10.4064/aa163-4-3