Polynomials assuming only local prime powers
Number Theory
2025-11-12 v1
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 -th powers, where 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 -th powers of polynomials.
Cite
@article{arxiv.2511.08100,
title = {Polynomials assuming only local prime powers},
author = {Przemysław Koprowski},
journal= {arXiv preprint arXiv:2511.08100},
year = {2025}
}