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arXiv · 1601.04938

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

Xander Faber·Bianca Thompson
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Abstract

Using essentially only algebra, we give a proof that a cubic rational function over $\mathbb{C}$ with real critical points is equivalent to a real rational function. We also show that the natural generalization to $\mathbb{Q}_p$ fails for all $p$.

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Xander Faber, Bianca Thompson. 2016-01-19. On the field of definition of a cubic rational function and its critical points. https://arxiv.org/abs/1601.04938

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