Identical representation functions of linear forms

2025/06/04 by Sándor Z. Kiss, Kiss, Sándor, Csaba Sándor +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2506.03983

openalex publication_date 2025/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Unique representations of integers by linear forms
• On the Structure of Sets Which Have Coinciding Representation Functions
• Partitions of the set of nonnegative integers with the same\n representation functions
• Integer sets with identical representation functions

Cited by

• Flexible Catalysis

Related

• Partitions of the set of nonnegative integers with the same\n representation functions
• On the Structure of Sets Which Have Coinciding Representation Functions
• Representation functions in the set of natural numbers
• On the values of representation functions II
• Unique representations of integers by linear forms