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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Approximations of arithmetical functions by additive ones
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by János Galambos PDF
Proc. Amer. Math. Soc. 39 (1973), 19-25 Request permission

Abstract:

Let ${\varepsilon _p}(n) = 1$ or 0 according as $p|n$ or not. Since the functions ${\varepsilon _p}(n) - 1/p$ are quasi-orthogonal on the integers $1,2, \cdots ,N$ with the relative frequency as measure, the theory of orthogonal expansions suggests an approximation of arbitrary arithmetical functions by strongly additive ones. In the present note, the approximating additive functions are determined and a sufficient condition is given for an arithmetical function to have an asymptotic distribution. Examples are given to illustrate the result.
References
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 39 (1973), 19-25
  • MSC: Primary 10K20
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0311614-5
  • MathSciNet review: 0311614