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Dynamical Systems and Uniform Distribution of Sequences

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From Arithmetic to Zeta-Functions

Abstract

We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for establishing multidimensional van der Corput sets. This condition is applied to various examples.

Dedicated to the memory of Professor Wolfgang Schwarz

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Acknowledgements

This research work was done when the first author was a visiting professor at the Department of Analysis and Number Theory at Graz University of Technology. The author thanks the institution for its hospitality. For the realization of the present paper the first author received support from the Conseil Régional de Lorraine.

The second author acknowledges support of the project F 5510-N26 within the special research area “Quasi Monte-Carlo Methods and applications” founded by the Austrian Science Fund.

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Correspondence to Robert F. Tichy .

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Madritsch, M.G., Tichy, R.F. (2016). Dynamical Systems and Uniform Distribution of Sequences. In: Sander, J., Steuding, J., Steuding, R. (eds) From Arithmetic to Zeta-Functions. Springer, Cham. https://doi.org/10.1007/978-3-319-28203-9_17

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