Higher-degree Chowla conjecture for the Liouville function

Establish the Chowla conjecture for the Liouville function for integer polynomials of degree greater than one that are not of the form c g(x)^2, namely prove that the associated Liouville-function sums are o(x).

Background

The paper recalls Sarvadaman Chowla’s conjecture that, for every integer polynomial F(x) not expressible as c g(x)^2, the sum of the Liouville function over the values F(n) satisfies $\sum_{n\le x}\lambda(F(n))=o(x)$. The linear case is equivalent to the prime number theorem in arithmetic progressions, whereas the authors explicitly identify the higher-degree case as unresolved. This is the classical integer-polynomial problem that motivates the function-field and truncated-Möbius results developed in the paper.