@article{Furstenberg1977,
  author  = {Furstenberg, H.},
  title   = {Ergodic behavior of diagonal measures and a theorem of {Szemer{\'e}di} on arithmetic progressions},
  journal = {Journal d'Analyse Math{\'e}matique},
  volume  = {31},
  pages   = {204--256},
  year    = {1977},
  doi     = {10.1007/BF02813304},
  url     = {https://doi.org/10.1007/BF02813304}
}

@article{Sarkozy1978I,
  author  = {S{\'a}rk{\"o}zy, A.},
  title   = {On difference sets of sequences of integers. {I}},
  journal = {Acta Mathematica Academiae Scientiarum Hungaricae},
  volume  = {31},
  number  = {1--2},
  pages   = {125--149},
  year    = {1978},
  doi     = {10.1007/BF01896079},
  url     = {https://doi.org/10.1007/BF01896079}
}

@article{PSS1988,
  author  = {Pintz, J. and Steiger, W. L. and Szemer{\'e}di, E.},
  title   = {On sets of natural numbers whose difference set contains no squares},
  journal = {Journal of the London Mathematical Society},
  series  = {2},
  volume  = {37},
  number  = {2},
  pages   = {219--231},
  year    = {1988},
  doi     = {10.1112/jlms/s2-37.2.219},
  url     = {https://doi.org/10.1112/jlms/s2-37.2.219}
}

@article{BloomMaynard2022,
  author        = {Bloom, Thomas F. and Maynard, James},
  title         = {A new upper bound for sets with no square differences},
  journal       = {Compositio Mathematica},
  volume        = {158},
  number        = {8},
  pages         = {1777--1798},
  year          = {2022},
  doi           = {10.1112/S0010437X22007679},
  url           = {https://doi.org/10.1112/S0010437X22007679},
  note          = {arXiv version 2, February 24, 2021},
  eprint        = {2011.13266},
  archivePrefix = {arXiv},
  primaryClass  = {math.NT}
}

@misc{GreenSawhney2025,
  author        = {Green, Ben and Sawhney, Mehtaab},
  title         = {New bounds for the {Furstenberg--S{\'a}rk{\"o}zy} theorem},
  year          = {2025},
  eprint        = {2411.17448},
  archivePrefix = {arXiv},
  primaryClass  = {math.NT},
  doi           = {10.48550/arXiv.2411.17448},
  url           = {https://arxiv.org/abs/2411.17448v2},
  howpublished  = {\href{https://arxiv.org/abs/2411.17448v2}{arXiv:\allowbreak2411.17448v2}},
  note          = {Version 2, January 10, 2025}
}

@misc{Krachun2026,
  author        = {Krachun, Dmitry},
  title         = {Square-Difference-Free Sets beyond the Three-Quarter Barrier},
  year          = {2026},
  eprint        = {2608.01325},
  archivePrefix = {arXiv},
  primaryClass  = {math.CO},
  doi           = {10.48550/arXiv.2608.01325},
  url           = {https://arxiv.org/abs/2608.01325v1},
  howpublished  = {\href{https://arxiv.org/abs/2608.01325v1}{arXiv:\allowbreak2608.01325v1}},
  note          = {Version 1, August 2, 2026}
}

@article{FILS1978ReflectionI,
  author  = {Fr{\"o}hlich, J{\"u}rg and Israel, Robert B. and Lieb, Elliott H. and Simon, Barry},
  title   = {Phase transitions and reflection positivity. {I}. General theory and long range lattice models},
  journal = {Communications in Mathematical Physics},
  volume  = {62},
  number  = {1},
  pages   = {1--34},
  year    = {1978},
  doi     = {10.1007/BF01940327},
  url     = {https://doi.org/10.1007/BF01940327}
}

@article{ConlonLee2017Reflection,
  author        = {Conlon, David and Lee, Joonkyung},
  title         = {Finite reflection groups and graph norms},
  journal       = {Advances in Mathematics},
  volume        = {315},
  pages         = {130--165},
  year          = {2017},
  doi           = {10.1016/j.aim.2017.05.009},
  url           = {https://doi.org/10.1016/j.aim.2017.05.009},
  eprint        = {1611.05784},
  archivePrefix = {arXiv},
  primaryClass  = {math.CO}
}

@article{Ruzsa1984,
  author = {Ruzsa, I. Z.},
  title = {Difference sets without squares},
  journal = {Periodica Mathematica Hungarica},
  volume = {15},
  number = {3},
  pages = {205--209},
  year = {1984},
  doi = {10.1007/BF02454169},
  url = {https://doi.org/10.1007/BF02454169}
}

@misc{BeigelGasarch2008,
  author = {Beigel, Richard and Gasarch, William},
  title = {Square-Difference-Free Sets of Size {$\Omega(n^{0.7334\ldots})$}},
  year = {2008},
  eprint = {0804.4892},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  url = {https://arxiv.org/abs/0804.4892v3},
  howpublished = {\href{https://arxiv.org/abs/0804.4892v3}{arXiv:\allowbreak0804.4892v3}},
  note = {Version 3, May 8, 2008}
}

@article{Lewko2015,
  author = {Lewko, Mark},
  title = {An improved lower bound related to the {Furstenberg--S{\'a}rk{\"o}zy} theorem},
  journal = {Electronic Journal of Combinatorics},
  volume = {22},
  number = {1},
  pages = {Paper P1.32, 6 pp.},
  year = {2015},
  doi = {10.37236/4656},
  url = {https://doi.org/10.37236/4656}
}
@misc{AdajarEtAl2026,
  author = {Adajar, Carlo Francisco E. and Agrawal, Rishika and Choudhuri, Mukul Rai and Chuah, Chian Yeong and Fan, Steve and Hegde, Swaroop and Lott, Andrew and Nandakumar, Krishnamohan and Ponagandla, Nagendar Reddy},
  title = {Extensions of the {Furstenberg--S\'ark\"ozy} theorem via the arithmetic level-$d$ inequality},
  year = {2026},
  eprint = {2605.16216},
  archivePrefix = {arXiv},
  primaryClass = {math.NT},
  doi = {10.48550/arXiv.2605.16216},
  url = {https://arxiv.org/abs/2605.16216v2},
  howpublished = {\href{https://arxiv.org/abs/2605.16216v2}{arXiv:\allowbreak2605.16216v2}},
  note = {Version 2, August 28, 2026}
}

@article{FrohlichLieb1978,
  author = {Fr{\"o}hlich, J{\"u}rg and Lieb, Elliott H.},
  title = {Phase transitions in anisotropic lattice spin systems},
  journal = {Communications in Mathematical Physics},
  volume = {60},
  number = {3},
  pages = {233--267},
  year = {1978},
  doi = {10.1007/BF01612891},
  url = {https://doi.org/10.1007/BF01612891}
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@article{Hatami2010,
  author = {Hatami, Hamed},
  title = {Graph norms and {Sidorenko}'s conjecture},
  journal = {Israel Journal of Mathematics},
  volume = {175},
  pages = {125--150},
  year = {2010},
  note = {Theorem locators refer to \href{https://arxiv.org/abs/0806.0047v1}{arXiv:\allowbreak0806.0047v1}},
  doi = {10.1007/s11856-010-0005-1},
  url = {https://doi.org/10.1007/s11856-010-0005-1},
  eprint = {0806.0047},
  archivePrefix = {arXiv}
}

@article{MontgomeryVaughan1973,
  author  = {Montgomery, H. L. and Vaughan, R. C.},
  title   = {The large sieve},
  journal = {Mathematika},
  volume  = {20},
  number  = {2},
  pages   = {119--134},
  year    = {1973},
  doi     = {10.1112/S0025579300004708},
  url     = {https://doi.org/10.1112/S0025579300004708}
}

@article{DeLaPenaMontgomerySmith1995,
  author        = {de la Pe{\~n}a, Victor H. and Montgomery-Smith, Stephen J.},
  title         = {Decoupling inequalities for the tail probabilities of multivariate {$U$}-statistics},
  journal       = {The Annals of Probability},
  volume        = {23},
  number        = {2},
  pages         = {806--816},
  year          = {1995},
  doi           = {10.1214/aop/1176988291},
  url           = {https://arxiv.org/abs/math/9309211v2},
  eprint        = {math/9309211},
  archivePrefix = {arXiv},
  note          = {Section locators refer to \href{https://arxiv.org/abs/math/9309211v2}{arXiv:\allowbreak math/9309211v2}}
}