HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

On polynomials that equal binary cubic forms.

Abstract : Let $F(x)$ be a cubic polynomial with rational integral coefficients with the property that, for all sufficiently large integers $n,\,F(n)$ is equal to a value assumed, through integers $u, v$, by a given irreducible binary cubic form $f(u,v)=au^3+bu^2v+cuv^2+dv^3$ with rational integral coefficients. We prove that then $F(x)=f(u(x),v(x))$, where $u=u(x), v=v(x)$ are linear binomials in $x$.
Document type :
Journal articles
Complete list of metadata

Cited literature [3 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01111461
Contributor : Ariane Rolland Connect in order to contact the contributor
Submitted on : Friday, January 30, 2015 - 1:59:39 PM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Saturday, September 12, 2015 - 6:45:54 AM

File

29Article1.pdf
Explicit agreement for this submission

Identifiers

Collections

Citation

C Hooley. On polynomials that equal binary cubic forms.. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2006, Volume 29 - 2006, pp.1 - 17. ⟨10.46298/hrj.2006.153⟩. ⟨hal-01111461⟩

Share

Metrics

Record views

25

Files downloads

305