Chowla's polynomial conjecture for the Liouville function

Let λ\lambda be the Liouville function. Let f(x)Z[x]f(x)\in\mathbb Z[x] be a polynomial that is not of the form cg(x)2cg(x)^2, where cZc\in\mathbb Z and g(x)Z[x]g(x)\in\mathbb Z[x]. Chowla's polynomial conjecture.

n=1xλ(f(n))=O(x).\sum_{n=1}^{x}\lambda(f(n))=O(x).

This is one of the two conjectures of Chowla highlighted by the paper, and no resolution is supplied; it remains open.

Sources & referencesView supporting material

Primary source

el Houcein el Abdalaoui, “On the Erdös flat polynomials problem, Chowla conjecture and Riemann Hypothesis”, arXiv:1609.03435 (2017).

Additional references

2 papers in this index state this conjecture (2011–2016). The statement above is taken from the most recent of them; the others are arXiv:1109.3107.

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