Displaying similar documents to “An improved estimate on the distribution mod 1 of powers of real matrices”

Effective simultaneous approximation of complex numbers by conjugate algebraic integers

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...

Normalizing constants for a statistic based on logarithms of disjoint m-spacings

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].