On the asymptotic distribution of the powers of -matrices
V. Losert, W.-G. Nowak, R. F. Tichy (1982)
Compositio Mathematica
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V. Losert, W.-G. Nowak, R. F. Tichy (1982)
Compositio Mathematica
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W. Narkiewicz (1963)
Colloquium Mathematicae
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Walter Philipp (1975)
Acta Arithmetica
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Hugh Montgomery (1980)
Acta Arithmetica
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G. J. Rieger (1993)
Acta Arithmetica
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We study effectively the simultaneous approximation of n-1 different complex numbers by conjugate algebraic integers of degree n over ℤ(√-1). This is a refinement of a result of Motzkin [2] (see also [3], p. 50) who has no estimate for the remaining conjugate. If the n-1 different complex numbers lie symmetrically about the real axis, then ℤ(√-1) can be replaced by ℤ. In Section 1 we prove an effective version of a Kronecker approximation theorem; we start with an...
Tom Meurman (1986)
Acta Arithmetica
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R. Baker (1973)
Acta Arithmetica
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M. Fisz (1954)
Studia Mathematica
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Franciszek Czekała (1996)
Applicationes Mathematicae
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The paper is concerned with the asymptotic normality of a certain statistic based on the logarithms of disjoint m-spacings. The exact and asymptotic mean and variance are computed in the case of uniform distribution on the interval [0,1]. This result is generalized to the case when the sample is drawn from a distribution with positive step density on [0,1].