Effective bounds for solutions of \(S\)-unit equations and of Thue-Mahler equations

DOI10.1006/jnth.1998.2245zbMath0926.11015OpenAlexW1968620667MaRDI QIDQ1273706

Yann Bugeaud

Publication date: 2 December 1999

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1998.2245

zbMATH Keywords

upper boundsThue-Mahler equationslinear form in logarithmseffective irrationality measure for algebraic numberssolutions of \(S\)-unit equations

Mathematics Subject Classification ID

Thue-Mahler equations (11D59) Measures of irrationality and of transcendence (11J82) Multiplicative and norm form equations (11D57)

Related Items (7)

UPPER BOUNDS FOR THE NUMBER OF SOLUTIONS TO QUARTIC THUE EQUATIONS ⋮ Solving 𝑆-unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture ⋮ Effective irrationality measures for real and p-adic roots of rational numbers close to 1, with an application to parametric families of Thue–Mahler equations ⋮ Effective simultaneous rational approximation to pairs of real quadratic numbers ⋮ Proof of the Baker-Feldman theorem via linear forms in two logarithms ⋮ Quartic Thue equations ⋮ Local positivity and effective Diophantine approximation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Siegel's lemma
• On the method of Thue-Siegel
• Diophantine approximation
• Effective lower bound for the \(p\)-adic distance between powers of algebraic numbers
• On the Thue-Siegel-Dyson theorem
• Logarithmic forms and group varieties.
• An effective lower bound for the height of algebraic numbers
• Bounds for the solutions of unit equations
• Bounds for the solutions of Thue-Mahler equations and norm form equations
• Linear forms in the logarithms of algebraic numbers
• RATIONAL APPROXIMATIONS TO 23 AND OTHER ALGEBRAIC NUMBERS
• Rational approximations to algebraic numbers

This page was built for publication: Effective bounds for solutions of \(S\)-unit equations and of Thue-Mahler equations