Random Thue and Fermat equations

Rainer Dietmann; Oscar Marmon

Acta Arithmetica, Tome 168 (2015), p. 189-200 / Harvested from The Polish Digital Mathematics Library

Résumé

We consider Thue equations of the form $a x^{k} + b y^{k} = 1$ , 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 $a x^{k} + b y^{k} + c z^{k} = 0$ of degree at least six.

Publié le : 2015-01-01

Zbl 06392171

EUDML-ID : urn:eudml:doc:279766

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     author = {Rainer Dietmann and Oscar Marmon},
     title = {Random Thue and Fermat equations},
     journal = {Acta Arithmetica},
     volume = {168},
     year = {2015},
     pages = {189-200},
     zbl = {06392171},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-2-6}
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Rainer Dietmann; Oscar Marmon. Random Thue and Fermat equations. Acta Arithmetica, Tome 168 (2015) pp. 189-200. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-2-6/