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arXiv · 1903.11311

The level of pairs of polynomials

Alberto F. Boix·Marc Paul Noordman·Jaap Top
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Abstract

Given a polynomial $f$ with coefficients in a field of prime characteristic $p$, it is known that there exists a differential operator that raises $1/f$ to its $p$th power. We first discuss a relation between the `level' of this differential operator and the notion of `stratification' in the case of hyperelliptic curves. Next we extend the notion of level to that of a pair of polynomials. We prove some basic properties and we compute this level in certain special cases. In particular we present examples of polynomials $g$ and $f$ such that there is no differential operator raising $g/f$ to its $p$th power.

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Alberto F. Boix, Marc Paul Noordman, Jaap Top. 2019-03-27. The level of pairs of polynomials. https://doi.org/10.1080/00927872.2020.1759614

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