Theses and Dissertations from UMD

Permanent URI for this communityhttp://hdl.handle.net/1903/2

New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM

More information is available at Theses and Dissertations at University of Maryland Libraries.

Browse

Filters

20241

Settings

Author: search.filters.author.Hirsh, JordanSubject: search.filters.subject.Images

Search Results

Now showing 1 - 1 of 1
  • No Thumbnail Available
    Item
    Polynomials with Equal Images over Number Fields
    (2024) Hirsh, Jordan; Washington, Lawrence C; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    Chapman and Ponomarenko [1] characterized when two polynomials f, g ∈ Q[x] have thesame image f(Z) = f(Z). We extend this result to rings of integers in number fields. In particular, if K is a finite extension of Q and O is the ring of algebraic integers in K, we characterize when polynomials f, g ∈ K[x] satisfy f(O) = g(O). As part of our proof, we give a variant of Hilbert’s irreducibility theorem.