Add to ORKGUsing the Thue-Siegel method, we obtain effective improvements on Liouville's irrationality measure for certain one-parameter families of algebraic numbers, defined by equations of the type (t-a)Q(t)+P(t)=0. We apply these to some corresponding Diophantine equations. We obtain bounds for the size of solutions, which depend polynomially on a, and bounds for the number of these solutions, which are independent of a and in some cases even independent of the degree of the equation
In this paper we provide bounds for the size of the solutions of some Diophantine equation
AbstractWe sharpen a technique of Gelfond to show that, in a sense, the only possible gap-free seque...
In this article we establish two new results on quantitative Diophantine approximation for one-param...
Using the Thue–Siegel method, we obtain effective improvements on Liouville’s irrationality measure ...
RésuméRecently, Bombieri and Bombieri and Cohen have developped a new method in effective diophantin...
In this paper we provide bounds for the size of the solutions of some Diophantine equation
AbstractWe apply Schlickewei's recent result on the S-unit equation to show that certain purely expo...
Given quantities $\Delta_1,\Delta_2,\dots\geqslant 0$, a fundamental problem in Diophantine approxim...
Let α be an algebraic number of degree d ≥ 3 and let K be the algebraic number field Q(α). When ε is...
In this paper, we simplify and improve the constant, $c$, that appears in effective irrationality me...
AbstractIn this paper, we use the method of Thue and Siegel, based on explicit Pade approximations t...
In this article we formalize some results of Diophantine approximation, i.e. the approximation of an...
We relate a previous result of ours on families of diophantine equations having only trivial solutio...
Suppose that λ1, λ2, λ3, λ4, λ5 are nonzero real numbers, not all of the same sign, λ1/λ2 is irratio...
to be published by Springer Verlag, Special volume in honor of Serge Lang, ed. Dorian Goldfeld, Jay ...
In this paper we provide bounds for the size of the solutions of some Diophantine equation
AbstractWe sharpen a technique of Gelfond to show that, in a sense, the only possible gap-free seque...
In this article we establish two new results on quantitative Diophantine approximation for one-param...
Using the Thue–Siegel method, we obtain effective improvements on Liouville’s irrationality measure ...
RésuméRecently, Bombieri and Bombieri and Cohen have developped a new method in effective diophantin...
In this paper we provide bounds for the size of the solutions of some Diophantine equation
AbstractWe apply Schlickewei's recent result on the S-unit equation to show that certain purely expo...
Given quantities $\Delta_1,\Delta_2,\dots\geqslant 0$, a fundamental problem in Diophantine approxim...
Let α be an algebraic number of degree d ≥ 3 and let K be the algebraic number field Q(α). When ε is...
In this paper, we simplify and improve the constant, $c$, that appears in effective irrationality me...
AbstractIn this paper, we use the method of Thue and Siegel, based on explicit Pade approximations t...
In this article we formalize some results of Diophantine approximation, i.e. the approximation of an...
We relate a previous result of ours on families of diophantine equations having only trivial solutio...
Suppose that λ1, λ2, λ3, λ4, λ5 are nonzero real numbers, not all of the same sign, λ1/λ2 is irratio...
to be published by Springer Verlag, Special volume in honor of Serge Lang, ed. Dorian Goldfeld, Jay ...
In this paper we provide bounds for the size of the solutions of some Diophantine equation
AbstractWe sharpen a technique of Gelfond to show that, in a sense, the only possible gap-free seque...
In this article we establish two new results on quantitative Diophantine approximation for one-param...