On totally reducible binary forms: II.

C Hooley (1)

1 University of Whales

Let $f$ be a binary form of degree $l\geq3$, that is, a product of linear forms with integer coefficients. The principal result of this paper is an asymptotic formula of the shape $n^{2/l}(C(f)+O(n^{-\eta_l+\varepsilon}))$ for the number of positive integers not exceeding $n$ that are representable by $f$; here $C(f)>0$ and $\eta_l>0$.

Mots clés: totally reducible binary forms; asymptotic formula; rational similarity of matrices; sets of automorphics

Domaines: Mathématiques [math]

C Hooley. On totally reducible binary forms: II.. Hardy-Ramanujan Journal, 2002, Volume 25 - 2002, pp.22-49. ⟨10.46298/hrj.2002.146⟩. ⟨hal-01109803⟩