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arXiv · 1605.06090

Analogs of the Shapiro Shapiro Conjecture in Positive Characteristic

Ryan Eberhart
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Abstract

Motivated by the Shapiro Shapiro conjecture, we consider the following: given a field $k$, under what conditions must a rational function with only $k$-rational ramification points be equivalent (after post-composition with a fractional linear transformation) to a rational function defined over $k$? The main results of this paper answer this question when $k$ has characteristic 2 or 3. We also show the insufficiency of several natural conditions in higher characteristic.

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Ryan Eberhart. 2016-05-19. Analogs of the Shapiro Shapiro Conjecture in Positive Characteristic. https://arxiv.org/abs/1605.06090

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