On Small Heights of Totally p-adic Numbers

Graduate Thesis Or Dissertation

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

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Attribute Name	Values
Creator	Stacy, Emerald T.
Abstract	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.
License	All rights reserved
Resource Type	Dissertation
Date Issued	2018-06-13
Degree Level	Doctoral
Degree Name	Doctor of Philosophy (Ph.D.)
Degree Field	Mathematics
Degree Grantor	Oregon State University
Commencement Year	2018
Advisor	Petsche, Clayton J.
Committee Member	Finch, David Flahive, Mary Maes, Cari Russ-Eft, Darlene
Academic Affiliation	Mathematics
Subject	Number theory
Rights Statement	In Copyright
Publisher	Oregon State University
Peer Reviewed	No
Language	English [eng]
Accessibility Feature	unknown

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