Titlebook: Number-Theoretic Analysis; Seminar, Vienna 1988 Edmund Hlawka,Robert F. Tichy Conference proceedings 1990 Springer-Verlag Berlin Heidelberg

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Number-Theoretic Analysis978-3-540-46864-6Series ISSN 0075-8434 Series E-ISSN 1617-9692

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0075-8434 Overview: 978-3-540-53408-2978-3-540-46864-6Series ISSN 0075-8434 Series E-ISSN 1617-9692

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Completely uniformly distributed sequences of matrices,It is proved that for almost all . × .-matrices . with largest eigenvalue .(.)>1 the sequence of powers (..). is completely uniformly distributed modulo 1, where .(.) are different positive integers. Furthermore a constructive example for a matrix . is given such that the sequence (..). is completely uniformly distributed.

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On digit expansions with respect to second order linear recurring sequences,A real number . is constructed, such that the sequence .. for . is uniformly distributed. The Hausdorff-dimension of some sets defined by decimal properties with respect to the ξ-expansion is computed.

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