Integral points and volume of integral-integral affine manifolds
Differential Geometry
2026-02-17 v3 Symplectic Geometry
Abstract
We give an elementary proof that, for a closed manifold with an integral-integral affine structure, its total volume and number of integral points coincide. The proof uses rational Ehrhart theory and elementary Fourier analysis to estimate the difference between the total volume and the number of integral points.
Cite
@article{arxiv.2508.17551,
title = {Integral points and volume of integral-integral affine manifolds},
author = {Oded Elisha and Yael Karshon and Yiannis Loizides},
journal= {arXiv preprint arXiv:2508.17551},
year = {2026}
}
Comments
10 pages. v3: Updating the introduction