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On Small Heights of Totally p-adic Numbers Public Deposited

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/0g354m24z

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  • The height of an algebraic number A is a measure of how arithmetically complicated A is. We say A is totally p-adic if the minimal polynomial of A splits completely over the field of p-adic numbers. In this paper, we investigate what can be said about the smallest nonzero height of a degree d totally p-adic number. In particular, we look at the cases that A is either contained within an abelian extension of the rationals, or has degree 2 or degree 3 over the rationals. Additionally, we determine an upper bound on the smallest limit point of the height of totally p-adic numbers for each fixed prime p.
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