On Almost Universal Ternary Inhomogeneous Quadratic Polynomials

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A fundamental question in the study of integral quadratic forms is the representation problem which asks for an effective determination of the set of integers represented by a given quadratic form. A related and equally interesting problem is the representation of integers by inhomogeneous quadratic polynomials. An inhomogeneous quadratic polynomial is a sum of a quadratic form and a linear form; it is called <em>almost universal</em> if it represents all but finitely many positive integers. This thesis gives a characterization of almost universal ternary inhomogeneous quadratic polynomials, <em>H(x)</em> whose quadratic parts are positive definite and anisotropic at exactly one prime. Imposing some other mild arithmetic conditions, we utilize the theory of quadratic lattices and primitive spinor exceptions to give a list of explicit conditions, under which <em>H(x)</em> is almost universal. In the final chapter, we will give some examples of almost universal quadratic polynomials given by mixed sums of polygonal numbers.

    Item Description
    Name(s)
    Thesis advisor: Chan, Wai Kiu, 1967-
    Date
    May 01, 2013
    Extent
    98 pages
    Language
    eng
    Genre
    Physical Form
    electronic
    Rights and Use
    In Copyright – Non-Commercial Use Permitted
    Digital Collection
    PID
    ir:2241