The Probability That a Random Monic p-adic Polynomial Splits

@article{Buhler2006ThePT,
  title={The Probability That a Random Monic p-adic Polynomial Splits},
  author={Joe Buhler and Daniel Goldstein and David Moews and Joel Rosenberg},
  journal={Experimental Mathematics},
  year={2006},
  volume={15},
  pages={21 - 32}
}
Let R be a complete discrete valuation ring with finite residue field, and let rn be the probability that a random monic polynomial over R of degree n factors over R into linear factors. We study rn in detail. Among other things, we show that rn satisfies an interesting recursion, make a conjecture on the asymptotic behavior of rn as n goes to infinity, and prove the conjecture in the case that the residue field has two elements. 
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