Sets with almost coinciding representation functions

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

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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