Arithmetic dynamical questions with local rationality conditions

Graduate Thesis Or Dissertation

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Citeable URL: https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/s4655q75n

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Attribute Name	Values
Creator	Noytaptim, Chatchai
Abstract	We introduce a numerical criterion which allows us to bound the degree of any algebraic integer having all of Galois conjugates in an interval of length less than 4. Using this criterion, we study two arithmetic dynamical questions with local rationality conditions. First, we classify all unicritical polynomials defined over the maximal totally real algebraic extension of rational numbers. Second, we classify all quadratic unicritical polynomials defined over rational numbers which have finitely many totally real (respectively, totally p-adic) preperiodic points. We also explicitly compute totally real preperiodic points of some quadratic unicritical polynomials defined over rational numbers. Our strategy uses tools from complex and p-adic potential theory and dynamics.
License	All rights reserved
Resource Type	Dissertation
Date Issued	2023-05-23
Degree Level	Doctoral
Degree Name	Doctor of Philosophy (Ph.D.)
Degree Field	Mathematics
Degree Grantor	Oregon State University
Commencement Year	2023
Advisor	Petsche, Clayton
Committee Member	Dascaliuc, Radu Guo, Ren Schmidt, Thomas
Academic Affiliation	Mathematics
Subject	Number Theory and Dynamical Systems
Rights Statement	In Copyright
Publisher	Oregon State University
Peer Reviewed	No
Language	English [eng]

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