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Random Thue and Fermat equations

Rainer Dietmann, Oscar Marmon (2015)

Acta Arithmetica

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.

Rational points on curves

Michael Stoll (2011)

Journal de Théorie des Nombres de Bordeaux

This is an extended version of an invited lecture I gave at the Journées Arithmétiques in St. Étienne in July 2009.We discuss the state of the art regarding the problem of finding the set of rational points on a (smooth projective) geometrically integral curve  C over  . The focus is on practical aspects of this problem in the case that the genus of  C is at least  2 , and therefore the set of rational points is finite.

Currently displaying 1 – 10 of 10

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