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Proceedings of the American Mathematical Society

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Representation of 0 as $ \sum \sp{N}\sb{K=-N}\,\varepsilon \sb{k}k$


Author: J. H. van Lint
Journal: Proc. Amer. Math. Soc. 18 (1967), 182-184
MSC: Primary 10.25
DOI: https://doi.org/10.1090/S0002-9939-1967-0205964-8
MathSciNet review: 0205964
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Abstract: If $ {\varepsilon _k}$ are independent identically distributed random variables with values 0 and $ 1$, each with probability $ \tfrac{1} {2}$ then

$\displaystyle P\left( {\sum\limits_{k = - N}^{ + N} {{\varepsilon _k}k = 0} } \right) \sim {\left( {\frac{3} {\pi }} \right)^{1/2}}{N^{ - 3/2}}.$


References [Enhancements On Off] (What's this?)

  • [1] A. Sárközy and E. Szemerédi, Über ein Problem von Erdös und Moser, Acta. Arith. 11 (1965), 205-208. MR 0182619 (32:102)

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DOI: https://doi.org/10.1090/S0002-9939-1967-0205964-8
Article copyright: © Copyright 1967 American Mathematical Society

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