Familles d'\'equations de Thue associ\'ees \`a un sous-groupe de rang 1 d'unit\'es totalement r\'eelles d'un corps de nombres

DOI10.1090/CONM/655/13225arXiv1505.06656MaRDI QIDQ6262079

Michel Waldschmidt, Claude Levesque

Publication date: 25 May 2015

Abstract: Let $F$ be an irreducible binary form attached to a number field $K$ of degree $geq3$. Let $epsilonotin-1,1$ be a totally real unit of $K$. By twisting $F$ with the powers $epsilo{n}^a$ of $epsilon$, ($ainmathbfZ$), we obtain an infinite family $F_a$ of binary forms. Let $minmathbfZ$. We give an effective bound for $max|a|,log|x|,log|y|$ when $a,x,y$ are rational integers satisfying $F_a(x,y)=m$ with $xyot=0$.

Mathematics Subject Classification ID

Thue-Mahler equations (11D59) Cubic and quartic Diophantine equations (11D25) Exponential Diophantine equations (11D61) Higher degree equations; Fermat's equation (11D41)

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