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The van der Corput Method

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Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2213))

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Abstract

A sequence of real numbers (u n ) is said to be uniformly distributed modulo 1 if for all interval I of length |I| < 1, we have

$$\displaystyle \lim _{N\rightarrow +\infty } \frac {1}{N} \#\{n: \ 1\leqslant n \leqslant N,\ u_n \in I \bmod 1\} = |I|. $$

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References

  1. S. Graham, G. Kolesnik, Van der Corput’s Method of Exponential Sums. London Mathematical Society Lecture Note Series, vol. 126 (Cambridge University Press, Cambridge, 1991)

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Authors and Affiliations

  1. Aix Marseille Université, CNRS, Centrale Marseille, Institut de Mathématiques de Marseille, I2M – UMR 7373, Marseille, France

    Joël Rivat

Authors
  1. Joël Rivat
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Correspondence to Joël Rivat .

Editor information

Editors and Affiliations

  1. CNRS UMR 7373, Institut de Mathématiques de Marseille, Marseille, France

    Sébastien Ferenczi

  2. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń, Poland

    Joanna Kułaga-Przymus

  3. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń, Poland

    Mariusz Lemańczyk

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Rivat, J. (2018). The van der Corput Method. In: Ferenczi, S., Kułaga-Przymus, J., Lemańczyk, M. (eds) Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics. Lecture Notes in Mathematics, vol 2213. Springer, Cham. https://doi.org/10.1007/978-3-319-74908-2_8

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