Fonctions arithmétiques et formes binaires irréductibles de degré 3

2014/08/09 by Armand Lachand, Lachand, Armand · 1 citation
Mathematics · #Analytic Number Theory Research #Algebraic Geometry and Number Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1408.2111

Abstract

Let F(X₁,X₂)∈ℤ[X₁,X₂] be an irreducible binary form of degree 3 and h an arithmetic function. We give some estimates for the average order ∑_\substack|n₁|≤ x,|n₂|≤ xh(F(n₁,n₂)) when h satisfy certain conditions. As an application, we provide some asymptotic formula for the number of y-friable values of F(n₁,n₂) when the variables n₁,n₂ lies in the square [1,x]² and uniformly in the region exp(\fraclog x(loglog x)^1/2-ε)≤ y≤ x. This improves a result of Balog, Blomer, Dartyge and Tenenbaum (2012).

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