MINIMAL POLYNOMIAL DYNAMICS ON THE p-ADIC INTEGERS

초록

In this paper, we present a method of characterizing minimal polynomials on the ring Zp 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 polyno-mials on Zp in terms of their coefficients, provided that two prescribed prerequisites for minimality are satisfied.

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