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2006 The Probability That a Random Monic p-adic Polynomial Splits
Joe Buhler, Daniel Goldstein, David Moews, Joel Rosenberg
Experiment. Math. 15(1): 21-32 (2006).

Abstract

Let {\small $R$} be a complete discrete valuation ring with finite residue field, and let {\small $r_n$} be the probability that a random monic polynomial over {\small $R$} of degree {\small $n$} factors over {\small $R$} into linear factors. We study {\small $r_n$} in detail. Among other things, we show that {\small $r_n$} satisfies an interesting recursion, make a conjecture on the asymptotic behavior of {\small $r_n$} as {\small $n$} goes to infinity, and prove the conjecture in the case that the residue field has two elements.

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Joe Buhler. Daniel Goldstein. David Moews. Joel Rosenberg. "The Probability That a Random Monic p-adic Polynomial Splits." Experiment. Math. 15 (1) 21 - 32, 2006.

Information

Published: 2006
First available in Project Euclid: 16 June 2006

zbMATH: 1113.11069
MathSciNet: MR2229382

Subjects:
Primary: 11S05

Keywords: p-adic , polynomial , splits completely

Rights: Copyright © 2006 A K Peters, Ltd.

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Vol.15 • No. 1 • 2006
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