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Filtering by: Advisor Swisher, Holly Remove constraint Advisor: Swisher, Holly Committee Member Petsche, Clayton Remove constraint Committee Member: Petsche, Clayton

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  • Zeros of Replicable Functions

    Creator:
    Toomey, Benjamin J.
    Abstract:
    Following the work of Asai, Kaneko, and Ninomiya for Faber polynomials associated to the modular group, and Bannai, Kojima, and Miezaki's partial proof for the case of the Fricke group of level 2, we show that the zeros of certain modular functions for some low-level genus zero groups associated to...
    Resource Type:
    Dissertation
    Full Text:
    : Zeros of Replicable Functions Abstract approved: Holly M. Swisher Following the work of Asai, Kaneko

  • 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:
    Functions Abstract approved: Holly Swisher In this dissertation, we consider two problems in number

  • Zeros of Certain Combinations of Products of Eisenstein Series

    Creator:
    Klangwang, Jetjaroen
    Abstract:
    In this dissertation, we begin by presenting the result of F. K. C. Rankin and Swinnerton-Dyer on the location of the zeros of the Eisenstein series for the full modular group in the standard fundamental domain. Their simple but beautiful argument shows that all zeros are located on the lower...
    Resource Type:
    Dissertation
    Full Text:
    Certain Combinations of Products of Eisenstein Series Abstract approved: Holly M. Swisher In this

  • 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
    Full Text:
    , Cranks, and Frobenius Representations Abstract approved: Holly M. Swisher We generalize overpartition

  • Periodicity and Partition Congruences

    Creator:
    Al-Saedi, Ali Hammood
    Abstract:
    In this note, we generalize recent work of Mizuhara, Sellers, and Swisher that gives a method for establishing restricted plane partition congruences based on a bounded number of calculations. Using periodicity for partition functions, our extended technique could be a useful tool to prove congruences for certain types of combinatorial...
    Resource Type:
    Dissertation
    Full Text:
    Partition Congruences Abstract approved: Holly M. Swisher In this note, we generalize recent work of