Random Thue and Fermat equations

2014/11/12 by Rainer Dietmann, Dietmann, Rainer, Oscar Marmon +1
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1411.3194

version 2 (one typo fixed and one reference added); 11 pages; to appear in Acta Arithmetica

arxiv created 2014/12/12 · arxiv updated 2014/12/15

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.

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