منابع مشابه
On the quadratic Lagrange spectrum
We study the quadratic Lagrange spectrum defined by Parkkonen and Paulin by considering the approximation by elements of the orbit of a given real quadratic irrational number for the action by homographies and anti-homographies of PSL2(Z) on R ∪ {∞}. Our approach is based on the theory of continued fractions.
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As is often the case, some results get rediscovered over time. In particular, some rather striking results of Lagrange are often recreated. For instance, in [6], a result pertaining to the Pell equation for a prime discriminant was recast in the light of nonabelian cohomology groups. Yet, in [1], the authors acknowledged the fact that the result “has been discovered before,” and provided an ele...
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Let γ = (1+ √ 5)/2 denote the golden ratio. H. Davenport and W. M. Schmidt showed in 1969 that, for each non-quadratic irrational real number ξ, there exists a constant c > 0 with the property that, for arbitrarily large values of X , the inequalities |x0| ≤ X, |x0ξ − x1| ≤ cX , |x0ξ − x2| ≤ cX admit no non-zero solution (x0, x1, x2) ∈ Z. Their result is best possible in the sense that, convers...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2013
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-013-1230-1