Image for the paper "On the distribution of quadratic residues"

LCP

Quadratic residues

Combinatorics

Additive combinatorics sheds light on the distribution of the set of squares in the prime field, revealing a new upper bound for the number of gaps.

On the distribution of quadratic residues

In press Finite Fields and Their Applications (2025)

I. Shkredov

Arxiv
aXi

In our paper, we apply additive-combinatorial methods to study the distribution of the set of squares  in the prime field. We obtain the best upper bound on the number of gaps in  at the moment and generalize this result for sets with small doubling.

In press Finite Fields and Their Applications (2025)

I. Shkredov