English

A new upper bound on Ruzsa's number on the Erd\H os-Tur\'{a}n conjecture

Number Theory 2023-08-30 v6

Abstract

In this note, we show that the Ruzsa number RmR_m is bounded by 192192 for any positive integer mm, which improved the prior bound Rm288R_m\le 288 given by Y.--G. Chen in 2008.

Keywords

Cite

@article{arxiv.2307.12311,
  title  = {A new upper bound on Ruzsa's number on the Erd\H os-Tur\'{a}n conjecture},
  author = {Yuchen Ding and Lilu Zhao},
  journal= {arXiv preprint arXiv:2307.12311},
  year   = {2023}
}

Comments

We make up some gaps pointed out by Professor Yong--Gao Chen