Almost 2-regular quinary quadratic forms

Abstract

A (positive definite integral) quadratic form is called almost n-regular if it globally represents all but finitely many quadratic forms of rank n that are locally represented up to isometry.

In this thesis, we discuss the finiteness of primitive almost 2-regular quinary quadratic forms up to isometry. We prove that there are finitely many almost 2-regular quinary quadratic forms that represent all integers. We also prove that there are finitely many primitive almost 2-regular quinary quadratic forms having an odd core prime. We discuss the finiteness of primitive almost 2-regular quinary quadratic forms which have 2 as the only core prime.