Random Thue and Fermat equations

• Autorzy: Rainer Dietmann , Oscar Marmon
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11G35: Varieties over global fields
• 11G50: Heights
• 11E76: Forms of degree higher than two
• 11D41: Higher degree equations; Fermat's equation
• 14G05: Rational points
• 11D45: Counting solutions of Diophantine equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 167
• Numer: 2
• Strony: 189-200

Daty

wydano

2015

Twórcy

autor

Rainer Dietmann

• Department of Mathematics, Royal Holloway, University of London, Egham TW20 0EX, UK

autor

Oscar Marmon

• Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstr. 3-5, 37073 Göttingen, Germany

Identyfikatory

DOI

10.4064/aa167-2-6