A note on the lower bound of representation functions

被引：0

作者：

Jiang, Xing-Wang ^{[1
]}

Sandor, Csaba ^{[2
,3
]}

Yang, Quan-Hui ^{[4
]}

机构：

[1] Nanjing Normal Univ, Sch Math Sci, Inst Math, Nanjing 210023, Peoples R China

[2] Budapest Univ Technol & Econ, Inst Math, Budapest, Hungary

[3] Budapest Univ Technol & Econ, MTA BME Lendulet Arithmet Combinator Res Grp, H-1529 Budapest, Hungary

[4] Nanjing Univ Informat Sci & Technol, Sch Math & Stat, Nanjing 210044, Peoples R China

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2021年 / 17卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Partition; representation function; Thue-Morse sequence; Sarkozy's problem; ADDITIVE PROPERTIES; NATURAL-NUMBERS; PARTITIONS; VALUES;

D O I：

10.1142/S179304212150086X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a set A of nonnegative integers, let R-2(A,n) denote the number of solutions to n = a + a ' with a,a 'is an element of A, a < a '. Let A(0) be the Thue-Morse sequence and B-0 = N\A(0). Let A subset of N and N be a positive integer such that R-2(A,n) = R-2(N\A,n) for all n >= 2N - 1. Previously, the first author proved that if |A boolean AND A(0)| = +infinity and |A boolean AND B-0| = +infinity, then R-2(A,n) >= n+3/56N-52 - 1 for all n >= 1. In this paper, we prove that the above lower bound is nearly best possible. We also get some other results.

引用

页码：2243 / 2250

页数：8

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