# On the density at integer points of a system comprising an inhomogeneous quadratic form and a linear form

## TL;DR

This paper extends the Oppenheim conjecture to inhomogeneous quadratic and linear forms in three variables, using dynamics on affine lattices to establish density results at integer points.

## Contribution

It provides a new inhomogeneous analogue of the Oppenheim conjecture for systems involving quadratic and linear forms in three variables.

## Key findings

- Established density of integer points for the system using affine lattice dynamics.
- Extended classical results to inhomogeneous forms in a new setting.
- Proved an analogue of the Oppenheim conjecture for this specific system.

## Abstract

We prove an analogue of the Oppenheim conjecture for a system comprising an inhomogeneous quadratic form and a linear form in $3$ variables using dynamics on the space of affine lattices.