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arXiv · 2511.08100

Polynomials assuming only local prime powers

Przemysław Koprowski
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Abstract

We study the class of polynomials that map a local field (i.e., the completion of a number field at a non-Archimedean place) into the subset of its $p$-th powers, where $p$ is the residue characteristic of the field in question. We present a characterization of such polynomials and show that this class is always much broader than the class of $p$-th powers of polynomials.

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Przemysław Koprowski. 2025-11-11. Polynomials assuming only local prime powers. https://arxiv.org/abs/2511.08100

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