S-unit equations over number fields

DOI10.1007/BF01233421zbMath0711.11017OpenAlexW2004723509MaRDI QIDQ922582

Hans Peter Schlickewei

Publication date: 1990

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143828

zbMATH Keywords

gap principleS-unit equations

Mathematics Subject Classification ID

Units and factorization (11R27) Exponential Diophantine equations (11D61)

Related Items

The number of solutions of decomposable form equations ⋮ On a problem of A. M. Odlyzko on algebraic units of bounded degree ⋮ Finite polynomial orbits in finitely generated domains ⋮ Integral points of projective spaces omitting hyperplanes over function fields of positive characteristic ⋮ Arithmetic properties of positive integers with fixed digit sum ⋮ Quantitative estimates for the size of an intersection of sparse automatic sets ⋮ Mixing properties of commuting nilmanifold automorphisms ⋮ \(S\)-parts of sums of terms of linear recurrence sequences ⋮ On the quenched functional CLT in random sceneries ⋮ Uniqueness conjecture on simultaneous Pell equations ⋮ A new mean ergodic theorem for tori and recurrences ⋮ Ledrappier’s system is almost mixing of all orders ⋮ On the Diophantine equation \(p^{x_1} - p^{x_2} = q^{y_1} - q^{y_2}\) ⋮ 𝑆-integral points of ℙⁿ-{2𝕟+1 hyperplanes in general position over number fields and function fields} ⋮ Mixing automorphisms of compact groups and a theorem of Schlickewei ⋮ Polynomial cycles in certain rings of rationals ⋮ Planar dynamical systems with pure Lebesgue diffraction spectrum ⋮ Multiplicities of algebraic linear recurrences ⋮ Exponential diophantine equations and the irrationality of certain real numbers ⋮ A game with two players choosing the coefficients of a polynomial ⋮ Upper bounds for the numbers of solutions of unit equations in two unknowns

Cites Work

• On equations in S-units and the Thue-Mahler equation
• The \(\mathfrak p\)-adic Thue-Siegel-Roth-Schmidt theorem
• Zur Approximation algebraischer Zahlen. I: Über den grössten Primteiler binärer Formen
• An explicit upper bound for the number of solutions of the S-unit equation.
• The number of subspaces occurring in the p-adic subspace theorem in diophantine approximation.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item