Type: Article
Publication Date: 2018-01-01
Citations: 5
DOI: https://doi.org/10.5802/aif.3189
In this article, we give some estimates for the average order, over the values of the cubic form X 1 3 +2X 2 3 , for some multiplicative functions h satisfying certain conditions. We provide an asymptotic formula for the number of y-friable values of n 1 3 +2n 2 3 , valid in an unbounded range. Our method also applies to some oscillating multiplicative functions like the Mœbius function μ : this gives another proof of the Chowla conjecture for the form X 1 3 +2X 2 3 recently proved by Helfgott in the more general case of binary and irreducible cubic forms.