MINIMAL POLYNOMIAL DYNAMICS ON THE p-ADIC INTEGERS

In this paper, we present a method of characterizing minimal polynomials on the ring p of p-adic integers in terms of their coefficients for an arbitrary prime p. We first revisit and provide alternative proofs of the known minimality criteria given by Larin [11] for p = 2 and Durand and Paccaut [6]...

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Bibliographic Details
Published inJournal of the Korean Mathematical Society Vol. 60; no. 1; pp. 1 - 32
Main Author Sangtae Jeong
Format Journal Article
LanguageKorean
Published 2023
Subjects
minimal
ergodic
p-adic integers
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Summary:In this paper, we present a method of characterizing minimal polynomials on the ring p of p-adic integers in terms of their coefficients for an arbitrary prime p. We first revisit and provide alternative proofs of the known minimality criteria given by Larin [11] for p = 2 and Durand and Paccaut [6] for p = 3, and then we show that for any prime p ≥ 5, the proposed method enables us to classify all possible minimal polynomials on p in terms of their coefficients, provided that two prescribed prerequisites for minimality are satisfied.
Bibliography:KISTI1.1003/JNL.JAKO202311854434233
ISSN:0304-9914