Various approaches for the study of the complexity of some families of pseudorandom subsets

Abstract

Studying randomness in different structures is important from the development of applications and theory. Dartyge, Mosaki and Sárközy (among others) have studied measures of randomness for families of subsets of integers. In this article, we improve results on the complexity of some families defined by polynomials, introducing new techniques from areas such as combinatorial geometry, geometry of numbers and additive combinatorics.