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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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An elementary method for estimating error terms in additive number theory
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by Elmer K. Hayashi
Proc. Amer. Math. Soc. 52 (1975), 55-59
DOI: https://doi.org/10.1090/S0002-9939-1975-0376586-8

Abstract:

Let ${R_k}(n)$ denote the number of ways of representing the integers not exceeding $n$ as the sum of $k$ members of a given sequence of nonnegative integers. Using only elementary methods, we prove a general theorem from which we deduce that, for every $\epsilon > 0$, \[ {R_k}(n) - c{n^\beta } \ne o({n^{\beta (1 - \beta )(1 - 1/k)/(1 - \beta + \beta /k) - \epsilon }})\] where $c$ is a positive constant and $0 < \beta < 1$.
References
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Bibliographic Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 55-59
  • MSC: Primary 10J99
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0376586-8
  • MathSciNet review: 0376586