Lattice simplices with a fixed positive number of interior lattice points: A nearly optimal volume bound

TL;DR

This paper establishes a nearly optimal upper volume bound for lattice simplices with a fixed positive number of interior lattice points, improving previous results significantly.

Contribution

It provides an explicit upper bound on the volume of such simplices that is close to the conjectural maximum, differing only by a linear factor in the dimension.

Findings

Derived an explicit volume bound close to the conjectural maximum.

Improved upon previous bounds by Pikhurko from 2001.

Bound differs from the conjecture by only a linear factor in the dimension.

Abstract

We give an explicit upper bound on the volume of lattice simplices with fixed positive number of interior lattice points. The bound differs from the conjectural sharp upper bound only by a linear factor in the dimension. This improves significantly upon the previously best results by Pikhurko from 2001.