{"docId":146,"paperId":146,"url":"https:\/\/hrj.episciences.org\/146","doi":"10.46298\/hrj.2002.146","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":36,"name":"Volume 25 - 2002"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01109803","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01109803v1","dateSubmitted":"2015-03-03 16:13:55","dateAccepted":"2015-06-12 16:05:46","datePublished":"2002-01-01 08:00:00","titles":{"en":"On totally reducible binary forms: II."},"authors":["Hooley, C"],"abstracts":{"en":"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 $\\eta_l>0$."},"keywords":[{"en":" asymptotic formula"},{"en":" rational similarity of matrices"},{"en":" sets of automorphics"},{"en":"totally reducible binary forms"},"[MATH] Mathematics [math]"]}