On the field of definition of a cubic rational function and its critical points

Using essentially only algebra, we give a proof that a cubic rational function over C with real critical points is equivalent to a real rational function. We also show that the natural generalization to Qp fails unless p=3.

Saved in:
Bibliographic Details
Published in:Journal of number theory 2016-10, Vol.167, p.1-6
Main Authors: Faber, Xander, Thompson, Bianca
Format: Article
Language:English
Subjects:
B. and M. Shapiro conjecture
Critical points
Cubic rational functions
Field of definition
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Using essentially only algebra, we give a proof that a cubic rational function over C with real critical points is equivalent to a real rational function. We also show that the natural generalization to Qp fails unless p=3.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2016.02.011