The lower bound of weighted representation function

2023/06/28 by Chen, Shi-Qiang
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2306.16025

Abstract

For any given set A of nonnegative integers and for any given two positive integers k₁,k₂, R_k1,k2(A,n) is defined as the number of solutions of the equation n=k₁a₁+k₂a₂ with a₁,a₂∈ A. In this paper, we prove that if integer k≥2 and set A⊆ℕ such that R_1,k(A,n)=R_1,k(ℕ∖ A,n) holds for all integers n≥ n₀, then R_1,k(A,n)≫ log n.

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