On the equation a³ + b³ⁿ = c²

Michael A. Bennett, et al. "On the equation a³ + b³ⁿ = c²." Acta Arithmetica 163.4 (2014): 327-343. <http://eudml.org/doc/279697>.

@article{MichaelA2014,
abstract = {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.},
author = {Michael A. Bennett, Imin Chen, Sander R. Dahmen, Soroosh Yazdani},
journal = {Acta Arithmetica},
keywords = {Fermat equations; Galois representations; Q-curves; multi-Frey techniques},
language = {eng},
number = {4},
pages = {327-343},
title = {On the equation a³ + b³ⁿ = c²},
url = {http://eudml.org/doc/279697},
volume = {163},
year = {2014},
}

TY - JOUR
AU - Michael A. Bennett
AU - Imin Chen
AU - Sander R. Dahmen
AU - Soroosh Yazdani
TI - On the equation a³ + b³ⁿ = c²
JO - Acta Arithmetica
PY - 2014
VL - 163
IS - 4
SP - 327
EP - 343
AB - 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.
LA - eng
KW - Fermat equations; Galois representations; Q-curves; multi-Frey techniques
UR - http://eudml.org/doc/279697
ER -