Browsing Mathematics Theses and Dissertations by Subject "Number Theory"

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  • A Special Family of Binary Forms, Their Invariant Theory, and Related Computations 
    Dethier, Christophe (University of Oregon, 2020-12-08)
    In this manuscript we study the family of diagonalizable forms, a special family of integral binary forms. We begin with a summary of definitions and known results relevant to binary forms, diagonalizable forms, Thue ...
  • Linear Recurrence Sequences in Diophantine Analysis 
    Bellah, Elisa (University of Oregon, 2022-10-04)
    Diophantine analysis is an area of number theory concerned with finding integral solutions to polynomial equations defined over the rationals, or more generally over a number field. In some cases, it is possible to associate ...
  • The Combinatorics of log-Coulomb Gases in p-Fields 
    Webster, Joe (University of Oregon, 2021-09-13)
    This thesis is based on the article [16], which studies the integral? ? ?a? ?b? s ρ(x1,...,xN) max|xi −xj| min|xi −xj| |xi −xj| ij dx1 ...dxN KN i<j i<j i<j where K is an arbitrary p-field, ρ is a well-behaved function ...

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