The Markoff spectrum
Marshall Hall (1971)
Acta Arithmetica
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Marshall Hall (1971)
Acta Arithmetica
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Andrzej Schinzel (1973)
Acta Arithmetica
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A. Bazylewicz (1976)
Acta Arithmetica
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Yehoram Gordon, Marius Junge (1999)
Studia Mathematica
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There exists an absolute constant such that for any n-dimensional Banach space E there exists a k-dimensional subspace F ⊂ E with k≤ n/2 such that . The concept of volume ratio with respect to -spaces is used to prove the following distance estimate for : .
K. Ramanathan (1984)
Acta Arithmetica
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D. Przeworska-Rolewicz (1969)
Studia Mathematica
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J. Radecki (1962)
Studia Mathematica
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Mahta Khosravi, John A. Toth (2005)
Annales de l'institut Fourier
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Let be the error term in Weyl’s law for a 3-dimensional Riemannian Heisenberg manifold. We prove that , where is a specific nonzero constant and is an arbitrary small positive number. This is consistent with the conjecture of Petridis and Toth stating that .The idea of the proof is to use the Poisson summation formula to write the error term in a form which can be estimated by the method of the stationary phase. The similar result will be also proven in the -dimensional case. ...