On a Question of Craven and a Theorem of Belyi
| dc.creator | Borisov, Alexandr | |
| dc.date | 2002-05-25 | |
| dc.date | 2002-12-01 | |
| dc.date.accessioned | 2026-07-07T04:48:42Z | |
| dc.date.available | 2026-07-07T04:48:42Z | |
| dc.description | In this elementary note we prove that a polynomial with rational coefficients divides the derivative of some polynomial which splits in $\Q$ if and only if all of its irrational roots are real and simple. This provides an answer to a question posed by Thomas Craven. Similar ideas also lead to a variation of the proof of Belyi's theorem that every algebraic curve defined over an algebraic number field admits a map to $P^1$ which is only ramified above three points. As it turned out, this variation was noticed previously by G. Belyi himself and Leonardo Zapponi. | |
| dc.description | Main theorem was generalized to include reducible polynomials. To appear in Proceedings of AMS | |
| dc.identifier | https://arxiv.org/abs/math/0205266 | |
| dc.identifier | http://arxiv.org/abs/math/0205266 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64152 | |
| dc.subject | Number Theory | |
| dc.subject | 11R99 | |
| dc.title | On a Question of Craven and a Theorem of Belyi | |
| dc.type | text |