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Polynomials assuming only local prime powers
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DOI：10.1080/00927872.2026.2634228.png)
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Abstract
En 中文
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 criterion characterizing such polynomials. Moreover, we show that this class is always much broader than the class of p-th powers of polynomials, which, in particular, has implications for the reduction of sums of squares of polynomials.
Keywords:
Local fields
polynomials
prime powers
valued fields
Journal
C
IF:
0.6
Papers:
271
Citations:
0