On the Liouville function on rational polynomial values
Volume 201 / 2021
Acta Arithmetica 201 (2021), 119-130
MSC: 11N32, 11G05, 11D09, 11D25.
DOI: 10.4064/aa200706-31-5
Published online: 29 October 2021
Abstract
We extend a conjecture of Cassigne et al. concerning the behaviour of the Liouville function at integral polynomial values to the rational case. We solve the new conjecture for polynomials of degree at most $2$, and provide partial results for polynomials of degree $3$. We also make some remarks concerning polynomials of degree $4$.
