@article{Bernstein1929,
 author = {Serge Bernstein},
 title = {Sur les fonctions absolument monotones},
 journal = {Acta Mathematica},
 volume = {52},
 year = {1929},
 pages = {1--66},
 doi = {10.1007/BF02592679}
}

@article{CarneiroLittmannVaaler2013,
  author = {Carneiro, Emanuel and Littmann, Friedrich and Vaaler, Jeffrey D.},
  title = {Gaussian subordination for the {Beurling--Selberg} extremal problem},
  journal = {Transactions of the American Mathematical Society},
  volume = {365}, number = {7}, pages = {3493--3534}, year = {2013},
  doi = {10.1090/S0002-9947-2013-05716-9},
  url = {https://arxiv.org/abs/1008.4969v2}
}

@article{Cassels1959,
  author = {Cassels, J. W. S.},
  title = {On a problem of {Rankin} about the {Epstein} zeta-function},
  journal = {Proceedings of the Glasgow Mathematical Association},
  volume = {4}, number = {2}, pages = {73--80}, year = {1959},
  doi = {10.1017/S2040618500033906},
  note = {See corrigendum, volume 6 (1963), page 116, and the 1964 corrections by Ennola and Diananda}
}

@article{Cassels1963Corrigendum,
  author = {Cassels, J. W. S.},
  title = {Corrigendum},
  journal = {Proceedings of the Glasgow Mathematical Association},
  volume = {6}, number = {2}, pages = {116}, year = {1963},
  doi = {10.1017/S2040618500034833},
  note = {Corrigendum to ``On a problem of Rankin about the Epstein zeta-function''}
}

@article{CKMRV2022,
  author  = {Cohn, Henry and Kumar, Abhinav and Miller, Stephen D. and
             Radchenko, Danylo and Viazovska, Maryna},
  title   = {{Universal optimality of the $E_8$ and Leech lattices and
              interpolation formulas}},
  journal = {Annals of Mathematics},
  series  = {2},
  year    = {2022},
  volume  = {196},
  number  = {3},
  pages   = {983--1082},
  doi     = {10.4007/annals.2022.196.3.3},
  url     = {https://annals.math.princeton.edu/2022/196-3/p03}
}

@article{CohnDeCourcyIreland2018,
  author  = {Cohn, Henry and de Courcy-Ireland, Matthew},
  title   = {{The Gaussian core model in high dimensions}},
  journal = {Duke Mathematical Journal},
  year    = {2018},
  volume  = {167},
  number  = {13},
  pages   = {2417--2455},
  doi     = {10.1215/00127094-2018-0018},
  url     = {https://arxiv.org/abs/1603.09684v6}
}

@article{CohnElkies2003,
  author  = {Cohn, Henry and Elkies, Noam},
  title   = {{New upper bounds on sphere packings I}},
  journal = {Annals of Mathematics},
  series  = {2},
  year    = {2003},
  volume  = {157},
  number  = {2},
  pages   = {689--714},
  doi     = {10.4007/annals.2003.157.689},
  url     = {https://annals.math.princeton.edu/2003/157-2/p09}
}

@article{CohnKumar2007,
  author  = {Cohn, Henry and Kumar, Abhinav},
  title   = {{Universally optimal distribution of points on spheres}},
  journal = {Journal of the American Mathematical Society},
  year    = {2007},
  volume  = {20},
  number  = {1},
  pages   = {99--148},
  doi     = {10.1090/S0894-0347-06-00546-7},
  url     = {https://arxiv.org/abs/math/0607446v2}
}

@misc{CohnMiller2016,
  author = {Cohn, Henry and Miller, Stephen D.},
  title = {Some properties of optimal functions for sphere packing in dimensions {$8$} and {$24$}},
  year = {2016},
  eprint = {1603.04759},
  archivePrefix = {arXiv},
  primaryClass = {math.MG},
  note = {Version 1, March 15, 2016},
  url = {https://arxiv.org/abs/1603.04759v1}
}

@article{Diananda1964,
  author = {Diananda, P. H.},
  title = {Notes on two lemmas concerning the {Epstein} zeta-function},
  journal = {Proceedings of the Glasgow Mathematical Association},
  volume = {6}, number = {4}, pages = {202--204}, year = {1964},
  doi = {10.1017/S2040618500035036}
}

@article{Dubourdieu1940,
  author = {Dubourdieu, M. J.},
  title = {Sur un th{\'e}or{\`e}me de {M.} {S.} {Bernstein} relatif
           {\`a} la transformation de {Laplace-Stieltjes}},
  journal = {Compositio Mathematica},
  volume = {7},
  pages = {96--111},
  year = {1940},
  url = {https://www.numdam.org/item/CM_1940__7__96_0/}
}

@article{Ennola1964Lemma,
  author = {Ennola, Veikko},
  title = {A lemma about the {Epstein} zeta-function},
  journal = {Proceedings of the Glasgow Mathematical Association},
  volume = {6}, number = {4}, pages = {198--201}, year = {1964},
  doi = {10.1017/S2040618500035024}
}

@article{FaulhuberShafkulovskaZlotnikov2023,
  author  = {Faulhuber, Markus and Shafkulovska, Irina and Zlotnikov, Ilia},
  title   = {{A note on energy minimization in dimension 2}},
  journal = {Proceedings of the American Mathematical Society, Series B},
  year    = {2024},
  volume  = {11},
  pages   = {664--679},
  doi     = {10.1090/bproc/247},
  url     = {https://doi.org/10.1090/bproc/247}
}

@article{HardinTenpas2025,
  author = {Hardin, Douglas P. and Tenpas, Nathaniel J.},
  title = {Universally optimal periodic configurations in the plane},
  journal = {Discrete Analysis}, year = {2025},
  note = {Paper No. 26, 63 pp.},
  doi = {10.19086/da.144978},
  url = {https://arxiv.org/abs/2307.15822v4}
}

@misc{Leble2025,
  author = {Lebl{\'e}, Thomas},
  title = {The hexagonal lattice is universally locally optimal},
  year = {2025}, eprint = {2511.03353}, archivePrefix = {arXiv},
  note = {Version 1, submitted November 5, 2025},
  url = {https://arxiv.org/abs/2511.03353v1}
}

@article{Montgomery1988,
  author  = {Montgomery, Hugh L.},
  title   = {{Minimal theta functions}},
  journal = {Glasgow Mathematical Journal},
  year    = {1988},
  volume  = {30},
  number  = {1},
  pages   = {75--85},
  doi     = {10.1017/S0017089500007047},
  url     = {https://doi.org/10.1017/S0017089500007047}
}

@article{RadchenkoViazovska2019,
  author = {Radchenko, Danylo and Viazovska, Maryna},
  title = {Fourier interpolation on the real line},
  journal = {Publications Math{\'e}matiques de l'IH{\'E}S},
  volume = {129}, pages = {51--81}, year = {2019},
  doi = {10.1007/s10240-018-0101-z},
  url = {https://www.numdam.org/articles/10.1007/s10240-018-0101-z/}
}

@article{Rankin1953,
  author = {Rankin, R. A.},
  title = {A minimum problem for the {Epstein} zeta-function},
  journal = {Proceedings of the Glasgow Mathematical Association},
  volume = {1}, number = {4}, pages = {149--158}, year = {1953},
  doi = {10.1017/S2040618500035668}
}

@misc{Sardari2021,
  author = {Talebizadeh Sardari, Naser},
  title = {Higher {Fourier} interpolation on the plane},
  year = {2021},
  eprint = {2102.08753}, archivePrefix = {arXiv}, primaryClass = {math.NT},
  note = {Version 2, May 4, 2021},
  url = {https://arxiv.org/abs/2102.08753v2}
}

@misc{SharpPlanar2026,
  author = {{OpenAI}},
  title = {{A sharp Fourier certificate for planar circle packing}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-sharp-Fourier-certificate-for-planar-circle-packing-September-23-2026/paper.pdf}{OAI:A-sharp-Fourier-certificate-for-planar-circle-packing-September-23-2026}},
  year = {2026}
}

@misc{UniversalTriangular2026,
  author = {{OpenAI}},
  title = {{Universal optimality of the triangular lattice}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Universal-optimality-of-the-triangular-lattice-September-23-2026/paper.pdf}{OAI:Universal-optimality-of-the-triangular-lattice-September-23-2026}},
  year = {2026}
}

@article{TitiGarloff2019,
  author = {Titi, Jihad and Garloff, J{\"u}rgen},
  title = {Matrix methods for the tensorial {Bernstein} form},
  journal = {Applied Mathematics and Computation},
  volume = {346}, pages = {254--271}, year = {2019},
  doi = {10.1016/j.amc.2018.08.049},
  url = {https://www-home.htwg-konstanz.de/~garloff/AMC-2.pdf}
}

@article{Widder1931,
 author = {D. V. Widder},
 title = {Necessary and sufficient conditions for the representation of a function as a {Laplace} integral},
 journal = {Transactions of the American Mathematical Society},
 volume = {33},
 number = {4},
 year = {1931},
 pages = {851--892},
 doi = {10.1090/S0002-9947-1931-1501621-6}
}