Convergence results for systems of linear forms on cyclic groups, and periodic nilsequences

Pablo Candela, Olof Sisask

Given a positive integer $N$ and real number $\alpha \in [0,1]$, let $m(\alpha ,N)$ denote the minimum, over all sets $A\subset \mathbb{Z}/N\mathbb{Z}$ of size at least $\alpha N$, of the normalize…