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arXiv · 2506.03983

Identical representation functions of linear forms

Sándor Kiss·Csaba Sándor
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Abstract

For a set of natural numbers $A$, let $R_{A}(n)$ be the number of representations of a natural number $n$ as the sum of two terms from $A$. Many years ago, Nathanson studied the conditions for the set $A$ and $B$ of natural numbers that are needed to guarantee that $R_{A}(n) = R_{B}(n)$ for every positive integer $n$. In the last decades, similar questions have been studied by many authors. In this paper, we extend Nathanson's result to representation functions associated to linear forms and we study related problems.

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Sándor Kiss, Csaba Sándor. 2025-06-04. Identical representation functions of linear forms. https://arxiv.org/abs/2506.03983

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