Random Thue and Fermat equations

Rainer Dietmann, and Oscar Marmon. "Random Thue and Fermat equations." Acta Arithmetica 167.2 (2015): 189-200. <http://eudml.org/doc/279766>.

@article{RainerDietmann2015,
abstract = {We consider Thue equations of the form $ax^k + by^k = 1$, and assuming the truth of the abc-conjecture, we show that almost all locally soluble Thue equations of degree at least three violate the Hasse principle. A similar conclusion holds true for Fermat equations $ax^k + by^k + cz^k = 0$ of degree at least six.},
author = {Rainer Dietmann, Oscar Marmon},
journal = {Acta Arithmetica},
keywords = {Thue equations; Fermat equations; random Diophantine equations; Hasse principle; abc-conjecture},
language = {eng},
number = {2},
pages = {189-200},
title = {Random Thue and Fermat equations},
url = {http://eudml.org/doc/279766},
volume = {167},
year = {2015},
}

TY - JOUR
AU - Rainer Dietmann
AU - Oscar Marmon
TI - Random Thue and Fermat equations
JO - Acta Arithmetica
PY - 2015
VL - 167
IS - 2
SP - 189
EP - 200
AB - We consider Thue equations of the form $ax^k + by^k = 1$, and assuming the truth of the abc-conjecture, we show that almost all locally soluble Thue equations of degree at least three violate the Hasse principle. A similar conclusion holds true for Fermat equations $ax^k + by^k + cz^k = 0$ of degree at least six.
LA - eng
KW - Thue equations; Fermat equations; random Diophantine equations; Hasse principle; abc-conjecture
UR - http://eudml.org/doc/279766
ER -