scholarly journals Simultaneous Diophantine approximation: sums of squares and homogeneous polynomials

2019 ◽  
Vol 190 (1) ◽  
pp. 87-100
Author(s):  
Dmitry Kleinbock ◽  
Nikolay Moshchevitin
Keyword(s):  
Diophantine Approximation ◽  
Sums Of Squares ◽  
Homogeneous Polynomials ◽  
Simultaneous Diophantine Approximation

scholarly journals KHINTCHINE'S THEOREM AND TRANSFERENCE PRINCIPLE FOR STAR BODIES

2006 ◽  
Vol 02 (03) ◽  
pp. 431-453
Author(s):  
M. M. DODSON ◽  
S. KRISTENSEN
Keyword(s):  
Distance Function ◽  
Diophantine Approximation ◽  
Direct Proof ◽  
Distance Functions ◽  
Transference Principle ◽  
Simultaneous Diophantine Approximation ◽  
Star Bodies

Analogues of Khintchine's Theorem in simultaneous Diophantine approximation in the plane are proved with the classical height replaced by fairly general planar distance functions or equivalently star bodies. Khintchine's transference principle is discussed for distance functions and a direct proof for the multiplicative version is given. A transference principle is also established for a different distance function.

scholarly journals Vertical Shift and Simultaneous Diophantine Approximation on Polynomial Curves

2014 ◽  
Vol 58 (1) ◽  
pp. 1-26
Author(s):  
Faustin Adiceam
Keyword(s):  
Hausdorff Dimension ◽  
Diophantine Approximation ◽  
Rational Approximations ◽  
Vertical Shift ◽  
Polynomial Curves ◽  
Integer Coefficients ◽  
Simultaneous Diophantine Approximation ◽  
First Results

AbstractThe Hausdorff dimension of the set of simultaneously τ-well-approximable points lying on a curve defined by a polynomial P(X) + α, where P(X) ∈ ℤ[X] and α ∈ ℝ, is studied when τ is larger than the degree of P(X). This provides the first results related to the computation of the Hausdorff dimension of the set of well-approximable points lying on a curve that is not defined by a polynomial with integer coefficients. The proofs of the results also include the study of problems in Diophantine approximation in the case where the numerators and the denominators of the rational approximations are related by some congruential constraint.

ON THE SIMULTANEOUS DIOPHANTINE APPROXIMATION OF NEW PRODUCTS

Analysis ◽  
2000 ◽  
Vol 20 (4) ◽  
pp. 387-394 ◽  
Author(s):  
Peter Bundschuh ◽  
Keijo Väänänen
Keyword(s):  
Diophantine Approximation ◽  
New Products ◽  
Simultaneous Diophantine Approximation
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