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Corps de nombres algébriques d'anneau d'entiers monogène

Séminaire Delange-Pisot-Poitou. Théorie des nombres

Sur les générateurs des ordres monogènes des corps de nombres algébriques.

Seminaire de Théorie des Nombres de Bordeaux

Acta Arithmetica

Acta Arithmetica

Acta Arithmetica

Acta Arithmetica

Index form equations in quintic fields

Acta Arithmetica

The problem of determining power integral bases in algebraic number fields is equivalent to solving the corresponding index form equations. As is known (cf. Győry ), every index form equation can be reduced to an equation system consisting of unit equations in two variables over the normal closure of the original field. However, the unit rank of the normal closure is usually too large for practical use. In a recent paper Győry  succeeded in reducing index form equations to systems of unit...

Acta Arithmetica

Acta Arithmetica

Effective results for Diophantine equations over finitely generated domains

Acta Arithmetica

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 $f\left(x\right)=\delta {y}^{m}$ in x,y ∈ A, where f ∈ A[X], δ ∈ A∖0 and $m\in {ℤ}_{\ge 2}$. 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...

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