Convergence Results for Systems of Linear Forms on Cyclic Groups and Periodic Nilsequences
Convergence Results for Systems of Linear Forms on Cyclic Groups and Periodic Nilsequences
Given a positive integer $N$ and real number $\alpha\in [0, 1]$, let $m(\alpha,N)$ denote the minimum, over all sets $A\subseteq \mathbb{Z}_{N}$ of size at least $\alpha N$, of the normalized count of 3-term arithmetic progressions contained in $A$. A theorem of Croot states that $m(\alpha,N)$ converges as $N\to\infty$ through the …