Work

Squares and difference sets in finite fields

Year: 2013

Type: preprint

Abstract: For infinitely many primes $p=4k+1$ we give a slightly improved upper bound for the maximal cardinality of a set $B\subset \ZZ_p$ such that the difference set $B-B$ contains only quadratic residues. Namely, instead of the "trivial" bound $|B|\leq \sqrt{p}$ we prove $|B|\leq \sqrt{p}-1$, under suitable conditions on $p$. The new bound is valid for approximately three quarters of the primes $p=4k+1$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1305.0577

Authors: Bachoc, Christine, Ruzsa, Imre Z., Matolcsi, Mate

Institutions: HUN-REN Alfréd Rényi Institute of Mathematics, Institut de Mathématiques de Bordeaux, Hungarian Academy of Sciences

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4300526237

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