@article{Roth1951,
  author = {Roth, K. F.},
  title = {On a Problem of {Heilbronn}},
  journal = {Journal of the London Mathematical Society},
  volume = {26},
  number = {3},
  pages = {198--204},
  year = {1951},
  doi = {10.1112/jlms/s1-26.3.198}
}

@article{KPS1982,
  author = {Koml{\'o}s, J{\'a}nos and Pintz, J{\'a}nos and Szemer{\'e}di, Endre},
  title = {A Lower Bound for {Heilbronn}'s Problem},
  journal = {Journal of the London Mathematical Society (2)},
  volume = {25},
  number = {1},
  pages = {13--24},
  year = {1982},
  doi = {10.1112/jlms/s2-25.1.13}
}

@article{Schmidt1972,
  author = {Schmidt, Wolfgang M.},
  title = {On a Problem of {Heilbronn}},
  journal = {Journal of the London Mathematical Society (2)},
  volume = {4},
  number = {3},
  pages = {545--550},
  year = {1972},
  doi = {10.1112/jlms/s2-4.3.545}
}

@article{Roth1972a,
  author = {Roth, K. F.},
  title = {On a Problem of {Heilbronn}, {II}},
  journal = {Proceedings of the London Mathematical Society (3)},
  volume = {25},
  number = {2},
  pages = {193--212},
  year = {1972},
  doi = {10.1112/plms/s3-25.2.193}
}

@article{Roth1972b,
  author = {Roth, K. F.},
  title = {On a Problem of {Heilbronn}, {III}},
  journal = {Proceedings of the London Mathematical Society (3)},
  volume = {25},
  number = {3},
  pages = {543--549},
  year = {1972},
  doi = {10.1112/plms/s3-25.3.543}
}

@article{KPS1981,
  author = {Koml{\'o}s, J{\'a}nos and Pintz, J{\'a}nos and Szemer{\'e}di, Endre},
  title = {On {Heilbronn}'s Triangle Problem},
  journal = {Journal of the London Mathematical Society (2)},
  volume = {24},
  number = {3},
  pages = {385--396},
  year = {1981},
  doi = {10.1112/jlms/s2-24.3.385}
}

@misc{CPZ2023,
  author = {Cohen, Alex and Pohoata, Cosmin and Zakharov, Dmitrii},
  title = {A New Upper Bound for the {Heilbronn} Triangle Problem},
  year = {2023},
  eprint = {2305.18253},
  archivePrefix = {arXiv},
  note = {\href{https://arxiv.org/abs/2305.18253v1}{arXiv:2305.18253v1}, 29 May 2023},
  url = {https://arxiv.org/abs/2305.18253v1}
}

@article{CPZ2025,
  author = {Cohen, Alex and Pohoata, Cosmin and Zakharov, Dmitrii},
  title = {Lower Bounds for Incidences},
  journal = {Inventiones mathematicae},
  volume = {240},
  pages = {1045--1118},
  year = {2025},
  doi = {10.1007/s00222-025-01331-2},
  eprint = {2409.07658},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2409.07658v2}
}

@article{Zakharov2026,
  author = {Zakharov, Dmitrii},
  title = {Small Triangles},
  journal = {Journal of the London Mathematical Society},
  year = {2026},
  volume = {113},
  number = {3},
  pages = {e70447},
  doi = {10.1112/jlms.70447},
  url = {https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70447}
}

@article{Erdos1932,
  author = {Erd{\H o}s, Paul},
  title = {Beweis eines {Satzes} von {Tschebyschef}},
  journal = {Acta Litt. Sci. Szeged, Sect. Sci. Math.},
  volume = {5},
  pages = {194--198},
  year = {1932},
  url = {https://www.renyi.hu/~p_erdos/1932-01.pdf}
}

@book{LidlNiederreiter1994,
  author = {Lidl, Rudolf and Niederreiter, Harald},
  title = {Introduction to Finite Fields and their Applications},
  publisher = {Cambridge University Press},
  edition = {Second},
  year = {1994},
  doi = {10.1017/CBO9781139172769}
}

@article{Smith1861,
  author = {Smith, Henry John Stephen},
  title = {On Systems of Linear Indeterminate Equations and Congruences},
  journal = {Philosophical Transactions of the Royal Society of London},
  volume = {151},
  pages = {293--326},
  year = {1861},
  doi = {10.1098/rstl.1861.0016}
}

@article{SalemSpencer1942,
  author = {Salem, R. and Spencer, D. C.},
  title = {On Sets of Integers Which Contain No Three Terms in Arithmetical Progression},
  journal = {Proceedings of the National Academy of Sciences of the United States of America},
  volume = {28},
  number = {12},
  pages = {561--563},
  year = {1942},
  doi = {10.1073/pnas.28.12.561}
}

@article{Behrend1946,
  author = {Behrend, F. A.},
  title = {On Sets of Integers Which Contain No Three Terms in Arithmetical Progression},
  journal = {Proceedings of the National Academy of Sciences of the United States of America},
  volume = {32},
  number = {12},
  pages = {331--332},
  year = {1946},
  doi = {10.1073/pnas.32.12.331}
}

@article{Barlotti1956,
  author = {Barlotti, Adriano},
  title = {Un'osservazione sulle $k$-calotte degli spazi lineari finiti di dimensione tre},
  journal = {Bollettino dell'Unione Matematica Italiana (3)},
  volume = {11},
  number = {2},
  pages = {248--252},
  year = {1956},
  url = {https://www.bdim.eu/item?id=BUMI_1956_3_11_2_248_0}
}

@misc{Ellmann2025,
  author = {Ellmann, Gabor},
  title = {A Lower Bound for {Heilbronn}'s Triangle-Problem},
  year = {2025},
  eprint = {1703.03297},
  archivePrefix = {arXiv},
  note = {\href{https://arxiv.org/abs/1703.03297v12}{arXiv:1703.03297v12}, 12 November 2025},
  url = {https://arxiv.org/abs/1703.03297v12}
}

@misc{Agama2026,
  author = {Agama, Theophilus},
  title = {New Bounds for the {Heilbronn} Triangle Problem},
  year = {2026},
  eprint = {2006.05269},
  archivePrefix = {arXiv},
  note = {\href{https://arxiv.org/abs/2006.05269v13}{arXiv:2006.05269v13}, 6 May 2026},
  url = {https://arxiv.org/abs/2006.05269v13}
}

@misc{Henk2002,
  author = {Henk, Martin},
  title = {Successive Minima and Lattice Points},
  year = {2002},
  eprint = {math/0204158},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/math/0204158v1},
  note = {Theorem 1.3 (Minkowski's second theorem)}
}