Dirichlet's theorem on diophantine approximation. II
H. Davenport, Wolfgang Schmidt (1970)
Acta Arithmetica
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H. Davenport, Wolfgang Schmidt (1970)
Acta Arithmetica
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Łukasz Pańkowski (2010)
Acta Arithmetica
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Lior Fishman, David Simmons, Mariusz Urbański (2014)
Journal de Théorie des Nombres de Bordeaux
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In this paper, we extend the theory of simultaneous Diophantine approximation to infinite dimensions. Moreover, we discuss Dirichlet-type theorems in a very general framework and define what it means for such a theorem to be optimal. We show that optimality is implied by but does not imply the existence of badly approximable points.
Yasushige Watase (2015)
Formalized Mathematics
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In this article we formalize some results of Diophantine approximation, i.e. the approximation of an irrational number by rationals. A typical example is finding an integer solution (x, y) of the inequality |xθ − y| ≤ 1/x, where 0 is a real number. First, we formalize some lemmas about continued fractions. Then we prove that the inequality has infinitely many solutions by continued fractions. Finally, we formalize Dirichlet’s proof (1842) of existence of the solution [12], [1]. ...
Vitaly Bergelson, Inger J. Håland Knutson, Randall McCutcheon (2005)
Acta Arithmetica
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Charles Osgood (1969)
Acta Arithmetica
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Charles Osgood (1969)
Acta Arithmetica
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Jan Florek (2008)
Acta Arithmetica
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Yann Bugeaud, Bernard de Mathan (2009)
Acta Arithmetica
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Tomas Persson, Jörg Schmeling (2008)
Acta Arithmetica
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Yann Bugeaud, Nicolas Chevallier (2006)
Acta Arithmetica
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Demanze, O., Mouze, A. (2006)
International Journal of Mathematics and Mathematical Sciences
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Stephen Harrap (2012)
Acta Arithmetica
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