Higher Moments for Polynomial Chowla

Abstract

Let $\hat{I}»(n)$ be the Liouville function. We study the distribution of \[ \frac{1}{x^{1/2}}\sum_{x\leq n\leq 2x}λ(f(n)) \] over random polynomials $f$ of fixed degree $d$ and coefficients bounded in magnitude by $H$. In particular we prove that the first $d+1$ moments are Gaussian.

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