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Archiv der Mathematik

, Volume 79, Issue 3, pp 171–174 | Cite as

The distribution of dense Sidon subsets of $ \mathbb{Z}_m $

  • T. Schoen
Article
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Abstract.

Let \( S \subseteqq \mathbb{Z}_m \) be a Sidon set of cardinality \( \mid S \mid = m^{1 \over 2} + O(1) \). It is proved, in particular, that for any interval \( {\cal I} = \{a, a + 1, \ldots, a + \ell - 1\} \) in \( \mathbb{Z}_m \), \( 0 \leqq \ell \) < m, we have \( \big| {\mid S \cap {\cal I} \mid - \mid S \mid \ell/m} \big| = O(\mid S \mid^{1 \over 2}\textrm{ln}\, m) \).

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Copyright information

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  • T. Schoen
    • 1
  1. 1.Mathematisches Seminar, Universität zu Kiel, Ludewig-Meyn-Str. 4, D-24098 Kiel, Germany¶ and¶ Department of Discrete Mathematics, Adam Mickiewicz University, Poznań, PolandPoland

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