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  • An inner product on adelic measures

    Creator:
    Oberly, Peter J.
    Abstract:
    We define an inner product on a vector space of adelic measures over a number field $K$. We find that the norm induced by this inner product governs weak convergence at each place of $K$. The canonical adelic measure associated to a rational map is in this vector space, and...
    Resource Type:
    Dissertation
    Full Text:
    space of adelic measures over a number field K. We find that the norm induced by this inner product

  • Fourier Analysis and Equidistribution on the p-adic Integers

    Creator:
    Somasunderam, Naveen
    Abstract:
    In this dissertation, we use Fourier-analytic methods to study questions of equidistribution on the compact abelian group Zp of p-adic integers. In particu- lar, we prove a LeVeque-type Fourier analytic upper bound on the discrepancy of sequences. We establish p-adic analogues of the classical Dirichlet and Fejér kernels on R/Z,...
    Resource Type:
    Dissertation
    Full Text:
    absolute value, the p-adic field Qp, and the p-adic unit ball Zp which is a compact topological group that

  • 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:
    rank and crank generating functions to obtain k-fold vari- ants, and give a combinatorial

  • Enumeration Problems on Symmetries of Riemann Surfaces

    Creator:
    Camacho, Charles A.
    Abstract:
    We describe two combinatorial problems in the theory of automorphism groups of compact Riemann surfaces of genus two or greater: enumerate the topological actions of a finite group on surfaces and determine the set of genera of surfaces admitting such a group action, called the genus spectrum. We illustrate results...
    Resource Type:
    Dissertation
    Full Text:
    coefficients in a number field. Since the absolute Galois group can act on the coefficients, we obtain an

  • 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:
    Mizuhara, Sellers, and Swisher that gives a method for establishing restricted plane partition congruences

  • The structure of E6

    Creator:
    Wangberg, Aaron D.
    Abstract:
    A fundamental question related to any Lie algebra is to know its subalgebras. This is particularly true in the case of E6, an algebra which seems just large enough to contain the algebras which describe the fundamental forces in the Standard Model of particle physics. In this situation, the question...
    Resource Type:
    Dissertation
    Full Text:
    ) = pr for p, r ∈ G). A vector field X on G is left-invariant if, for any p, r ∈ G, it satisfies (dLrp−1