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Filtering by: Creator Petsche, Clayton Remove constraint Creator: Petsche, Clayton Committee Member Flahive, Mary Remove constraint Committee Member: Flahive, Mary

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  • On Small Heights of Totally p-adic Numbers

    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...
    Resource Type:
    Dissertation
    Full Text:
    Heights of Totally p-adic Numbers. Abstract approved: Clayton J. Petsche The height of an algebraic

  • Subalgebras of the Split Octonions

    Creator:
    Bentz, Lida
    Abstract:
    We classify the subalgebras of the split octonions, paying particular attention to the null subalgebras and their extensions.
    Resource Type:
    Capstone Project

  • Existence of Eta-Quotients for Squarefree Levels and Modular Type Supercongruences for Hypergeometric Functions

    Creator:
    Allen, Michael
    Abstract:
    In this dissertation, we consider two problems in number theory, both relating to modular forms. First we consider when a given modular form can be expressed as a quotient in Dedekind's $\eta$ function. Rouse and Webb \cite{RW} have determined the integers $N \leq 500$ such that the graded ring of...
    Resource Type:
    Dissertation
    Full Text:
    conversations and correspondences over the years; and finally my dissertation committee, Mary Flahive, Clayton

  • Overpartition Ranks, Cranks, and Frobenius Representations

    Creator:
    Morrill, Thomas
    Abstract:
    We generalize overpartition rank and crank generating functions to obtain k-fold variants, and give a combinatorial interpretation for each. The k-fold crank generating function is interpreted by extending the first and second residual cranks to a natural infinite family. The k-fold rank generating functions generate two families of buffered Frobenius...
    Resource Type:
    Dissertation