English

Refined Estimates Concerning Sumsets Contained in the Roots of Unity

Number Theory 2020-05-07 v3 Combinatorics

Abstract

We prove that the clique number of the Paley graph is at most p/2+1\sqrt{p/2} + 1, and that any supposed additive decompositions of the set of quadratic residues can only come from co-Sidon sets.

Keywords

Cite

@article{arxiv.1905.09134,
  title  = {Refined Estimates Concerning Sumsets Contained in the Roots of Unity},
  author = {Brandon Hanson and Giorgis Petridis},
  journal= {arXiv preprint arXiv:1905.09134},
  year   = {2020}
}

Comments

7 pages. The second version already included a corollary to Theorem 1.2 due to George Shakan that confirms Sarkozy's conjecture for almost all primes