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
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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