Squares and difference sets in finite fields

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 $p=4k+1$.

Locations

• Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) - View - PDF
• arXiv (Cornell University) - View - PDF
• CiteSeer X (The Pennsylvania State University) - View - PDF
• HAL (Le Centre pour la Communication Scientifique Directe) - View