A characterization of almost universal inhomogeneous quadratic polynomials
Speaker: Dr. Anna Haensch (Duquesne University and MPIM)
Time: 4.00PM
Date: Monday April 7th 2014
Location: Mathematics Seminar Room, Room AG 1.01, First Floor, Agriculture Building, UCD Belfield
Abstract:
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 almost universal if it represents all but finitely many positive integers. In this talk, I will give a characterization of almost universal ternary inhomogeneous quadratic polynomials, H(x), 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 H(x) is almost universal.
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