Work

Sets whose differences avoid squares modulo m

Year: 2020

Type: preprint

Abstract: We prove that if $\varepsilon(m)\to 0$ arbitrarily slowly, then for almost all $m$ and any $A\subset\mathbb{Z}_m$ such that $A-A$ does not contain non-zero quadratic residues we have $|A|\leq m^{1/2-\varepsilon(m)}.$

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2007.05774

Authors: Ford, Kevin, Gabdullin, Mikhail R.

Institutions: University of Illinois Urbana-Champaign, Steklov Mathematical Institute

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Ministry of Science and Higher Education of the Russian Federation

Awards: G2079737584, G2937397120, Primes, Divisors, and Permutations, G6444257319

OpenAlex ID: W3041738890

Cites: 14

Cited by:

Related to: 20