An effective Version of Faltings' Product Theorem.
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Anwendung des Perron'schen Beweises eines Satzes von Minkowski
J.F. Koksma (1939)
Mathematische Annalen
Billiard and diophantine approximation
Jan Florek (2008)
Acta Arithmetica
Effective simultaneous approximation of complex numbers by conjugate algebraic integers
G. J. Rieger (1993)
Acta Arithmetica
We study effectively the simultaneous approximation of n-1 different complex numbers by conjugate algebraic integers of degree n over ℤ(√-1). This is a refinement of a result of Motzkin [2] (see also [3], p. 50) who has no estimate for the remaining conjugate. If the n-1 different complex numbers lie symmetrically about the real axis, then ℤ(√-1) can be replaced by ℤ. In Section 1 we prove an effective version of a Kronecker approximation theorem; we start with an idea of H....
Inhomogeneous approximation with coprime integers and lattice orbits
Michel Laurent, Arnaldo Nogueira (2012)
Acta Arithmetica
Lower bounds for the number of integral polynomials with given order of discriminants
Vasili Bernik, Friedrich Götze, Olga Kukso (2008)
Acta Arithmetica
More on inhomogeneous diophantine approximation
Christopher G. Pinner (2001)
Journal de théorie des nombres de Bordeaux
For an irrational real number and real number we consider the inhomogeneous approximation constantvia the semi-regular negative continued fraction expansion of
Neuer Beweis eines Minkowskischen Satzes.
Edmund Landau (1931)
Journal für die reine und angewandte Mathematik
Notiz zu einem Satz über Diophantische Approximationen.
L. Schmetterer (1952)
Monatshefte für Mathematik
On a conjecture on exponential Diophantine equations
Mihai Cipu, Maurice Mignotte (2009)
Acta Arithmetica
On conjectures of Minkowski and Woods for n=8
R. J. Hans-Gill, Madhu Raka, Ranjeet Sehmi (2011)
Acta Arithmetica
On inhomogeneous Diophantine approximation and the Nishioka-Shiokawa-Tamura algorithm
Takao Komatsu (1998)
Acta Arithmetica
We obtain the values concerning using the algorithm by Nishioka, Shiokawa and Tamura. In application, we give the values (θ,1/2), (θ,1/a), (θ,1/√(ab(ab+4))) and so on when θ = (√(ab(ab+4)) - ab)/(2a) = [0;a,b,a,b,...].
On inhomogeneous diophantine approximation with some quasi-periodic expressions, II
Takao Komatsu (1999)
Journal de théorie des nombres de Bordeaux
We consider the values concerningwhere the continued fraction expansion of has a quasi-periodic form. In particular, we treat the cases so that each quasi-periodic form includes no constant. Furthermore, we give some general conditions satisfying .
On simultaneous inhomogeneous Diophantine approximation
Yann Bugeaud, Nicolas Chevallier (2006)
Acta Arithmetica
On the metric theory of inhomogeneous diophantine approximations
J. Kurzweil (1955)
Studia Mathematica
Simultaneous Diophantine approximation and asymptotic formulae on manifolds
Glyn Harman (2003)
Acta Arithmetica
Sopra una questione di approssimazione diofantea non lineare.
Marco Cugiani (1955)
Bollettino dell'Unione Matematica Italiana
Sur la répartition des sommets d'une ligne polygonale régulière non fermée
Roger Descombes (1956)
Annales scientifiques de l'École Normale Supérieure
Sur le théorème du produit
Gaël Rémond (2001)
Journal de théorie des nombres de Bordeaux
On donne des versions raffinées effectives du théorème du produit de G. Faltings et de son principal corollaire. Le théorème montre que si l’ensemble des zéros d’indice d’un polynôme multihomogène a une composante commune avec l’ensemble des zéros d’indice alors cette composante, sous-variété d’un produit d’espaces projectifs, est elle-même un produit à condition que les rapports des degrés de soient grands en fonction de . Le corollaire le plus utile implique que, sous une condition plus...
The View-Obstruction Problem for Spheres in ...5.
J.B. Wilker, V.C. Dumir, R.J. Hans-Gill (1996)
Monatshefte für Mathematik
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