On coefficient valuations of Eisenstein polynomials
Abstract
Let p > 2 be a prime, let n > m > 0. Let pin be the norm of zetapn - 1 under Cp-1, so that Z(p)[pin] | Z(p) is a purely ramified extension of discrete valuation rings of degree pn-1. The minimal polynomial of pin over Q(pim) is an Eisenstein polynomial; we give lower bounds for its coefficient valuations at pim. The function field analogue, as introduced by Carlitz and Hayes, is studied as well.
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