Sets with almost coinciding representation functions

Authors

  • S. Z. Kiss
  • E. Rozgonyi
  • C. Sandor

Keywords:

additive number theory, representation functions

Abstract

For a given integer \(n\) and a set \(\mathcal{S} \subseteq \mathbb{N}\) denote by \(R_{h,\mathcal{S}}^{(1)}(n)\) the number of solutions of the equation \(n=s_{i_1}+ \dots + s_{i_h}\), \(s_{i_j} \in \mathcal{S}\), \(j=1, \dots, h\). In this paper we determine all pairs \((\mathcal{A}, \mathcal{B})\), \(\mathcal{A}, \mathcal{B} \subseteq \mathbb{N}\) for which \(R_{3,\mathcal{A}}^{(1)}(n)=R_{3,\mathcal{B}}^{(1)}(n)\) from a certain point on. We discuss some related problems. 10.1017/S0004972713000518

Published

2013-12-02

Issue

Vol. 89 No. 1 (2014)

Section

Articles
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