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1
Content available remote

The number of solutions of linear equations in roots of unity

100%
Evertse J.-H.
Acta Arithmetica
|
1999
|
tom 89
|
nr 1
45-51
2
Content available remote

On resultant inequalities

100%
Evertse J.-H.
Acta Arithmetica
|
2002
|
tom 105
|
nr 1
67-101
3
Content available remote

An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma

100%
Evertse J.-H.
Acta Arithmetica
|
1995
|
tom 73
|
nr 3
215-248
4
Content available remote

Linear equations with unknowns from a multiplicative group in a function field

64%
Evertse J.-H., Zannier U.
Acta Arithmetica
|
2008
|
tom 133
|
nr 2
159-170
5
Content available remote

On two notions of complexity of algebraic numbers

64%
Bugeaud Y., Evertse J.-H.
Acta Arithmetica
|
2008
|
tom 133
|
nr 3
221-250
6
Content available remote

Effective results for Diophantine equations over finitely generated domains

51%
Bérczes A., Evertse J.-H., Győry K.
Acta Arithmetica
|
2014
|
tom 163
|
nr 1
71-100
EN
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 $f(x) = δy^m$ in x,y ∈ A, where f ∈ A[X], δ ∈ A∖{0} and $m ∈ ℤ_{≥ 2}$. 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 results imply that the solutions of these equations can be determined in principle. Further, we consider the Schinzel-Tijdeman equation $f(x) = δy^m$ where x,y ∈ A and $m ∈ ℤ_{≥2}$ are the unknowns and give an effective upper bound for m. Our results extend earlier work of Győry, Brindza and Végső, where the equations mentioned above were considered only for a restricted class of finitely generated domains.
7
Content available remote

On the number of pairs of binary forms with given degree and given resultant

51%
Bérczes A., Evertse J.-H., Győry K.
Acta Arithmetica
|
2007
|
tom 128
|
nr 1
19-54
8
Content available remote

Equal values of binary forms at integral points

51%
Evertse J.-H., Győry K., Shorey T. N., Tijdeman R.
Acta Arithmetica
|
1987
|
tom 48
|
nr 4
379-396
9
Content available remote

Effective results for linear equations in two unknowns from a multiplicative division group

51%
Bérczes A., Evertse J.-H., Győry K.
Acta Arithmetica
|
2009
|
tom 136
|
nr 4
331-349
10
Content available remote

On the number of equivalence classes of binary forms of given degree and given discriminant

51%
Bérczes A., Evertse J.-H., Győry K. a.
Acta Arithmetica
|
2004
|
tom 113
|
nr 4
363-399
11
Content available remote

On equations in two S-units over function fields of characteristic 0

44%
Evertse J.-H.
Acta Arithmetica
|
1986
|
tom 47
|
nr 3
233-253
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