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 , 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