% Bibliography for "One of zeta(7), zeta(9), ..., zeta(21) is irrational".
% Each entry was checked against the journal or DOI record, Math-Net.Ru, the SLC site or the arXiv record,
% as noted above it.

% Classical. Astérisque 61 (1979), 11--13.
@article{Apery1979,
  author  = {Ap\'ery, Roger},
  title   = {Irrationalit\'e de $\zeta(2)$ et $\zeta(3)$},
  journal = {Ast\'erisque},
  volume  = {61},
  year    = {1979},
  pages   = {11--13}
}

% arXiv:math/0008051; journal reference C. R. Acad. Sci. Paris Ser. I 331 (2000), no. 4, 267--270 (HAL hal-00125108).
@article{Rivoal2000,
  author  = {Rivoal, Tanguy},
  title   = {La fonction z\^eta de {R}iemann prend une infinit\'e de valeurs irrationnelles aux entiers impairs},
  journal = {C. R. Acad. Sci. Paris S\'er. I Math.},
  volume  = {331},
  number  = {4},
  year    = {2000},
  pages   = {267--270},
  note    = {arXiv:math/0008051}
}

% Inventiones record via DOI 10.1007/s002220100168.
@article{BallRivoal2001,
  author  = {Ball, Keith and Rivoal, Tanguy},
  title   = {Irrationalit\'e d'une infinit\'e de valeurs de la fonction z\^eta aux entiers impairs},
  journal = {Invent. Math.},
  volume  = {146},
  number  = {1},
  year    = {2001},
  pages   = {193--207},
  doi     = {10.1007/s002220100168}
}

% Math-Net.Ru record rm427; DOI 10.1070/RM2001v056n04ABEH000427.
@article{Zudilin2001,
  author  = {Zudilin, Wadim},
  title   = {One of the numbers $\zeta(5),\zeta(7),\zeta(9),\zeta(11)$ is irrational},
  journal = {Russian Math. Surveys},
  volume  = {56},
  number  = {4},
  year    = {2001},
  pages   = {774--776},
  doi     = {10.1070/RM2001v056n04ABEH000427}
}

% arXiv:math/0104221; DOI 10.4064/aa103-2-5.
@article{Rivoal2002,
  author  = {Rivoal, Tanguy},
  title   = {Irrationalit\'e d'au moins un des neuf nombres $\zeta(5),\zeta(7),\dots,\zeta(21)$},
  journal = {Acta Arith.},
  volume  = {103},
  number  = {2},
  year    = {2002},
  pages   = {157--167},
  doi     = {10.4064/aa103-2-5},
  note    = {arXiv:math/0104221}
}

% arXiv:math/0104249; Math-Net.Ru record im387 (Izv. Math. 66:3 (2002), 489--542; Russian original
% Izv. RAN Ser. Mat. 66:3, 49--102). Theorem numbers as in the arXiv version.
@article{Zudilin2002,
  author  = {Zudilin, Wadim},
  title   = {Irrationality of values of the {R}iemann zeta function},
  journal = {Izv. Math.},
  volume  = {66},
  number  = {3},
  year    = {2002},
  pages   = {489--542},
  note    = {arXiv:math/0104249}
}

% arXiv:math/0206176; Numdam record JTNB_2004__16_1_251_0; DOI 10.5802/jtnb.447.
% Section 8 (the derivative construction (8.2)--(8.4), Lemma 19) checked in the full text.
@article{Zudilin2004,
  author  = {Zudilin, Wadim},
  title   = {Arithmetic of linear forms involving odd zeta values},
  journal = {J. Th\'eor. Nombres Bordeaux},
  volume  = {16},
  number  = {1},
  year    = {2004},
  pages   = {251--291},
  doi     = {10.5802/jtnb.447},
  note    = {arXiv:math/0206176}
}

% arXiv:1801.09895 (SIGMA 14 (2018), 028).
@article{Zudilin2018,
  author  = {Zudilin, Wadim},
  title   = {One of the odd zeta values from $\zeta(5)$ to $\zeta(25)$ is irrational. {B}y elementary means},
  journal = {SIGMA Symmetry Integrability Geom. Methods Appl.},
  volume  = {14},
  year    = {2018},
  pages   = {Paper 028},
  note    = {arXiv:1801.09895}
}

% arXiv:1803.08905; Compositio record, DOI 10.1112/S0010437X1900722X.
@article{FSZ2019,
  author  = {Fischler, St\'ephane and Sprang, Johannes and Zudilin, Wadim},
  title   = {Many odd zeta values are irrational},
  journal = {Compos. Math.},
  volume  = {155},
  number  = {5},
  year    = {2019},
  pages   = {938--952},
  doi     = {10.1112/S0010437X1900722X},
  note    = {arXiv:1803.08905}
}

% arXiv:1803.03160; SLC record s81rivzud (Sem. Lothar. Combin. 81 (2020), Art. B81b).
@article{RivoalZudilin2020,
  author  = {Rivoal, Tanguy and Zudilin, Wadim},
  title   = {A note on odd zeta values},
  journal = {S\'em. Lothar. Combin.},
  volume  = {81},
  year    = {2020},
  pages   = {Art. B81b},
  note    = {arXiv:1803.03160}
}

% arXiv:2103.00904; published version on publi.math.unideb.hu/paper/4068.
@article{LaiZhou2022,
  author  = {Lai, Li and Zhou, Li},
  title   = {At least two of $\zeta(5),\zeta(7),\ldots,\zeta(35)$ are irrational},
  journal = {Publ. Math. Debrecen},
  volume  = {101},
  number  = {3--4},
  year    = {2022},
  pages   = {353--372},
  doi     = {10.5486/PMD.2022.9252},
  note    = {arXiv:2103.00904}
}

% Citation format from https://dlmf.nist.gov/help/cite.
@misc{DLMF,
  key          = {DLMF},
  title        = {{NIST} Digital Library of Mathematical Functions},
  howpublished = {\url{https://dlmf.nist.gov/}, Release 1.2.8 of 2026-09-15},
  note         = {F.~W.~J. Olver, A.~B. Olde~Daalhuis, D.~W. Lozier, B.~I. Schneider, R.~F. Boisvert,
                  C.~W. Clark, B.~R. Miller, B.~V. Saunders, H.~S. Cohl, and M.~A. McClain, eds.}
}

% arXiv:1910.09336; DOI 10.1145/3372885.3373824 (CPP 2020).
@inproceedings{Mathlib,
  author    = {{The mathlib Community}},
  title     = {The {L}ean mathematical library},
  booktitle = {Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP 2020)},
  publisher = {ACM},
  year      = {2020},
  pages     = {367--381},
  doi       = {10.1145/3372885.3373824},
  note      = {arXiv:1910.09336}
}

% Pinned in lake-manifest.json of the formalisation.
@misc{Mathlib4,
  author       = {{The mathlib Community}},
  title        = {mathlib4},
  howpublished = {\url{https://github.com/leanprover-community/mathlib4}},
  year         = {2026},
  note         = {Tag v4.35.0, commit 56a005855ea17e0b0958f73ec801ae140b0a1679}
}

@inproceedings{LeanFour,
  author    = {de Moura, Leonardo and Ullrich, Sebastian},
  title     = {The {L}ean 4 Theorem Prover and Programming Language},
  booktitle = {Automated Deduction -- CADE 28},
  series    = {Lecture Notes in Comput. Sci.},
  volume    = {12699},
  publisher = {Springer},
  year      = {2021},
  pages     = {625--635},
  doi       = {10.1007/978-3-030-79876-5_37}
}

@misc{PNTplus,
  author       = {Kontorovich, Alex and Tao, Terence and others},
  title        = {{PrimeNumberTheoremAnd}},
  howpublished = {\url{https://github.com/AlexKontorovich/PrimeNumberTheoremAnd}},
  year         = {2026},
  note         = {Lean project, Apache License 2.0; ported here through the \texttt{zeta5} repository of C.~Del Solar}
}

% Repository owner on GitHub: domino14. Formalises A. Fauzan's unrefereed proof that zeta(5) is irrational.
@misc{zeta5,
  author       = {Del Solar, C\'esar},
  title        = {$\zeta(5)$ is irrational: a {L}ean~4 formalization},
  howpublished = {\url{https://github.com/domino14/zeta5}},
  year         = {2026},
  note         = {Commit 3da8eb1b91f9a90a1c0b7959e845c060dbd16256, 23 September 2026}
}

@misc{BetaPaper,
  author       = {Krisman, Shawn},
  title        = {One of $\beta(4),\beta(6),\dots,\beta(36)$ is irrational},
  howpublished = {Manuscript with a Lean~4 formalisation, \url{https://github.com/telaviv/beta-irrationality}},
  year         = {2026},
  note         = {Tag v1.0, commit f8df497467901e09fa497553f00d8ffa4480a46d}
}

@misc{ZetaRepo,
  author       = {Krisman, Shawn},
  title        = {Lean formalisation: one of $\zeta(7),\zeta(9),\dots,\zeta(21)$ is irrational},
  howpublished = {\url{https://github.com/telaviv/zeta-irrationality}},
  year         = {2026},
  note         = {Tag v1.0}
}