The number of solutions of decomposable form equations.
Decomposable form equations with a small linear scattering.
The number of solutions of the Thue-Mahler equation.
On sums of -units and linear recurrences
An improvement of the quantitative subspace theorem
On the equation
On equations in two S-units over function fields of characteristic 0
An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma
The number of solutions of linear equations in roots of unity
On resultant inequalities
Finiteness criteria for decomposable form equations
Linear equations with unknowns from a multiplicative group in a function field
On two notions of complexity of algebraic numbers
Equal values of binary forms at integral points
Effective results for Diophantine equations over finitely generated domains
Let A be an arbitrary integral domain of characteristic 0 that is finitely generated over ℤ. We consider Thue equations F(x,y) = δ in x,y ∈ A, where F is a binary form with coefficients from A, and δ is a non-zero element from A, and hyper- and superelliptic equations in x,y ∈ A, where f ∈ A[X], δ ∈ A∖0 and . Under the necessary finiteness conditions we give effective upper bounds for the sizes of the solutions of the equations in terms of appropriate representations for A, δ, F, f, m. These...
On the number of equivalence classes of binary forms of given degree and given discriminant
On the number of pairs of binary forms with given degree and given resultant
Effective results for linear equations in two unknowns from a multiplicative division group
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