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Peer-reviewedCC BY-SA 4.0Symmetry, Integrability and Geometry: Methods and Applications

Integral Points and Volume of Integral-Integral Affine Manifolds

  • Oded Elisha1
  • Yael Karshon1
  • Yiannis Loizides2
  1. 1Tel Aviv University, Israel
  2. 2George Mason University, USA
Open at sourceDOICite

Abstract

Using rational Ehrhart theory and Fourier analysis, we give an elementary proof that the volume of a closed manifold equipped with an integral-integral affine structure equals the number of its integral points.

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Cite

BibTeXRIS
BibTeX
@article{elisha2026integral,
  title = {{Integral Points and Volume of Integral-Integral Affine Manifolds}},
  author = {Oded Elisha and Yael Karshon and Yiannis Loizides},
  journal = {Symmetry, Integrability and Geometry: Methods and Applications},
  year = {2026},
  month = oct,
  doi = {10.3842/sigma.2026.102},
  url = {https://sigma-journal.com/2026/102/},
  note = {CC BY-SA 4.0},
}
RIS
TY  - JOUR
TI  - Integral Points and Volume of Integral-Integral Affine Manifolds
AU  - Oded Elisha
AU  - Yael Karshon
AU  - Yiannis Loizides
PY  - 2026
DA  - 2026/10/29
JO  - Symmetry, Integrability and Geometry: Methods and Applications
DO  - 10.3842/sigma.2026.102
UR  - https://sigma-journal.com/2026/102/
AB  - Using rational Ehrhart theory and Fourier analysis, we give an elementary proof that the volume of a closed manifold equipped with an integral-integral affine structure equals the number of its integral points.
SN  - 1815-0659
ER  -