Back to Search
Start Over
On the values of representation functions II
- Publication Year :
- 2019
-
Abstract
- For a set $A$ of nonnegative integers, let $R_2(A,n)$ and $R_3(A,n)$ denote the number of solutions to $n=a+a'$ with $a,a'\in A$, $a<a'$ and $a\leq a'$, respectively. In this paper, we prove that, if $A\subseteq \mathbb{N}$ and $N$ is a positive integer such that $R_2(A,n)=R_2(\mathbb{N}\setminus A,n)$ for all $n\geq2N-1$, then for any $\theta$ with $0<\theta<\frac{2\log2-\log3}{42\log 2-9\log3}$, the set of integers $n$ with $R_2(A,n)=\frac{n}{8}+O(n^{1-\theta})$ has density one. The similar result holds for $R_3(A,n)$. These improve the results of the first author.<br />Comment: 12 pages
- Subjects :
- Mathematics - Number Theory
11B34, 11B83
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1904.10352
- Document Type :
- Working Paper