Some results on diophantine approximation related to Dirichlet's Theorem

1989 ◽  
pp. 137-149
Author(s):  
Hans G. Kopetzky
Keyword(s):  
Diophantine Approximation ◽  
Dirichlet’S Theorem ◽  
Dirichlet's Theorem

scholarly journals Dirichlet's Theorem in Function Fields

2017 ◽  
Vol 69 (3) ◽  
pp. 532-547 ◽  
Author(s):  
Arijit Ganguly ◽  
Anish Ghosh
Keyword(s):  
Diophantine Approximation ◽  
Function Fields ◽  
Dirichlet’S Theorem ◽  
Dirichlet's Theorem

AbstractWe studymetric Diophantine approximation for function fields, specifically, the problem of improving Dirichlet's theorem in Diophantine approximation.

Dirichlet's theorem on diophantine approximation

1978 ◽  
Vol 83 (1) ◽  
pp. 37-59 ◽  
Author(s):  
R. C. Baker
Keyword(s):  
Diophantine Approximation ◽  
Euclidean Plane ◽  
Dirichlet’S Theorem ◽  
Dirichlet's Theorem ◽  
Image Position

Let N take the values 1, 2, … A theorem of Dirichlet asserts that for any (x, y) in the Euclidean plane R2 the inequalityis soluble in integers q1, q2, p with 0 < max (|q1|, |q2|) ≤ N.

scholarly journals Dirichlet's theorem on diophantine approximation. II

1970 ◽  
Vol 16 (4) ◽  
pp. 413-424 ◽  
Author(s):  
H. Davenport ◽  
Wolfgang Schmidt
Keyword(s):  
Diophantine Approximation ◽  
Dirichlet’S Theorem ◽  
Dirichlet's Theorem

scholarly journals Dirichlet's theorem and diophantine approximation on manifolds

1990 ◽  
Vol 36 (1) ◽  
pp. 85-88 ◽  
Author(s):  
M.M Dodson ◽  
B.P Rynne ◽  
J.A.G Vickers
Keyword(s):  
Diophantine Approximation ◽  
Dirichlet’S Theorem ◽  
Dirichlet's Theorem

scholarly journals Dirichlet's theorem on diophantine approximation and homogeneous flows

2008 ◽  
Vol 2 (1) ◽  
pp. 43-62 ◽  
Author(s):  
Dmitry Kleinbock ◽  
◽  
Barak Weiss ◽  
Keyword(s):  
Diophantine Approximation ◽  
Dirichlet’S Theorem ◽  
Dirichlet's Theorem

scholarly journals Dirichlet's diophantine approximation theorem

1977 ◽  
Vol 16 (2) ◽  
pp. 219-224 ◽  
Author(s):  
T.W. Cusick
Keyword(s):  
General Solution ◽  
Recent Result ◽  
Diophantine Approximation ◽  
Approximation Theorem ◽  
Real Numbers ◽  
Simultaneous Diophantine Approximation ◽  
Dirichlet’S Theorem ◽  
Dirichlet's Theorem

One form of Dirichlet's theorem on simultaneous diophantine approximation asserts that if α1, α2, …, αn are any real numbers and m ≥ 2 is an integer, then there exist integers q, p1, p2, …, pn such that 1 ≤ q < m and |qαi.-pi| ≤ m–1/n holds for 1 < i < n. The paper considers the problem of the extent to which this theorem can be improved by replacing m–1/n by a smaller number. A general solution to this problem is given. It is also shown that a recent result of Kurt Mahler [Bull. Austral. Math. Soc. 14 (1976), 463–465] amounts to a solution of the case n = 1 of the above problem. A related conjecture of Mahler is proved.

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