Abstract or Additional Information
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. In the case of rational quadratic forms, Hasse¹s local-global principle gives a conclusive answer to the representation problem; currently no straightforward integral analogue of Hasse¹s result exists. In this talk I will discuss the related and equally interesting problem of representation 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. I will give a characterization of almost universal inhomogeneous quadratic polynomials, and I will explain the significance of almost universality in the context of finding an integral analogue to the Hasse principle.