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- W2809942626 abstract "Let $mgeq 2$ be a positive integer. Given a set $E(omega )subseteq mathbb{N}$ we define $r_{N}^{(m)}(omega )$ to be the number of ways to represent $Nin mathbb{Z}$ as any combination of sums $textit{ and }$ differences of $m$ distinct elements of $E(omega )$. In this paper, we prove the existence of a thick set $E(omega )$ and a positive constant $K$ such that $r_{N}^{(m)}(omega )<K$ for all $Nin mathbb{Z}$. This is a generalization of a known theorem by Erdős and Renyi. We also apply our results to harmonic analysis, where we prove the existence of certain thin sets." @default.
- W2809942626 created "2018-07-10" @default.
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- W2809942626 date "2014-04-09" @default.
- W2809942626 modified "2023-09-27" @default.
- W2809942626 title "A generalization of ErdH{o}s-R'enyi to $m$-fold sums and differences" @default.
- W2809942626 hasPublicationYear "2014" @default.
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