A note on the lower bound of representation functions-Reference-Cited by-同舟云学术

A note on the lower bound of representation functions

Published:2021-07-30 Issue:10 Volume:17 Page:2243-2250
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Jiang Xing-Wang¹,Sándor Csaba²³,Yang Quan-Hui⁴

Affiliation:

1. School of Mathematical Sciences, Institute of Mathematics, Nanjing Normal University, Nanjing 210023, P. R. China

2. Institute of Mathematics, Budapest University of Technology and Economics, Budapest, Hungary

3. MTA-BME Lendület Arithmetic Combinatorics Research Group, Budapest University of Technology and Economics, H-1529 B. O. Box, Budapest, Hungary

4. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China

Abstract

For a set [Formula: see text] of nonnegative integers, let [Formula: see text] denote the number of solutions to [Formula: see text] with [Formula: see text], [Formula: see text]. Let [Formula: see text] be the Thue–Morse sequence and [Formula: see text]. Let [Formula: see text] and [Formula: see text] be a positive integer such that [Formula: see text] for all [Formula: see text]. Previously, the first author proved that if [Formula: see text] and [Formula: see text], then [Formula: see text] for all [Formula: see text]. In this paper, we prove that the above lower bound is nearly best possible. We also get some other results.

Funder

National Natural Science Foundation of China

Project of Graduate Education Innovation of Jiangsu Province

NKFIH

Lend”ulet program of the Hungarian Academy of Sciences

National Natural Science Foundation for Youth of China

Natural Science Foundation of Jiangsu Province

Science Foundation of Jiangsu Province

Startup Foundation for Introducing Talent of NUIST

Publisher

World Scientific Pub Co Pte Ltd

Subject