A Characterization of almost universal ternary inhomogeneous quadratic polynomials with conductor 2

TL;DR

This paper characterizes almost universal ternary inhomogeneous quadratic polynomials with conductor 2, identifying conditions under which they represent all but finitely many positive integers.

Contribution

It provides a complete characterization of almost universal ternary inhomogeneous quadratic polynomials with conductor 2, a previously unexplored class.

Findings

Characterization criteria for almost universal polynomials

Conditions for representation of positive integers

Extension of known results to inhomogeneous cases

Abstract

An integral quadratic polynomial (with positive definite quadratic part) is called almost universal if it represents all but finitely many positive integers. In this paper, we provide a characterization of almost universal ternary quadratic polynomials with conductor 2.