Random Multiplicative Functions and Making Squares from Polynomial Values

Régis de la Bretèche, Victor Y. Wang, Max Wenqiang Xu

For a large family of polynomials $P(X)\in \mathbb{Z}[X]$, we prove central limit theorems for ${\sum }_{n\le N}f(P(n))$ for both Rademacher and extended Rademacher multiplicative fu…