% Bibliography for "One of beta(4), beta(6), ..., beta(36) is irrational".
% Every entry was checked on 2026-10-16 against the arXiv record, the journal/DOI record, or the
% official site (see the comment above each entry).

% arXiv:math/0104221; DOI 10.4064/aa103-2-5 (Acta Arith. contents of vol. 103).
@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}
}

% Bibliographic records (Newcastle repository, Steklov/MI RAS publication lists); DOI 10.1007/s00208-003-0420-2.
% Content (one of beta(2..14); infinitely many irrational even beta values) confirmed via Zudilin 2019 and Lai--Zhou.
@article{RivoalZudilin2003,
  author  = {Rivoal, Tanguy and Zudilin, Wadim},
  title   = {Diophantine properties of numbers related to {C}atalan's constant},
  journal = {Math. Ann.},
  volume  = {326},
  number  = {4},
  year    = {2003},
  pages   = {705--721},
  doi     = {10.1007/s00208-003-0420-2}
}

% arXiv:1804.09922 (journal reference on the arXiv page); DOI 10.1007/s12188-019-00203-w.
@article{Zudilin2019,
  author  = {Zudilin, Wadim},
  title   = {Arithmetic of {C}atalan's constant and its relatives},
  journal = {Abh. Math. Semin. Univ. Hambg.},
  volume  = {89},
  number  = {1},
  year    = {2019},
  pages   = {45--53},
  doi     = {10.1007/s12188-019-00203-w},
  note    = {arXiv:1804.09922}
}

% arXiv:math/0206176; Numdam record JTNB_2004__16_1_251_0; DOI 10.5802/jtnb.447.
% Section 8 "Linear forms in 1 and odd zeta values", 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:2103.00904 (v2, 18 Oct 2021; Thm. 6.1 = one of beta(2..10)); published version on publi.math.unideb.hu/paper/4068.
@article{LaiZhou2021,
  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}
}

% arXiv:1904.02402 (related DOI 10.1112/jlms.12290); volume/pages from the author's publication list.
@article{Fischler2020,
  author  = {Fischler, St\'ephane},
  title   = {Irrationality of values of {$L$}-functions of {D}irichlet characters},
  journal = {J. Lond. Math. Soc. (2)},
  volume  = {101},
  number  = {2},
  year    = {2020},
  pages   = {857--876},
  doi     = {10.1112/jlms.12290},
  note    = {arXiv:1904.02402}
}

% Inventiones record via DOI 10.1007/s002220100168; same details in the reference lists of Zudilin 2004 and
% Fischler--Sprang--Zudilin 2018.
@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}
}

% Citation format from https://dlmf.nist.gov/help/cite (Release 1.2.8 of 2026-09-15).
@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}
}

@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; the formalisation uses files from commit
                  a5154676af9aa3095150ee410cdda80555aa0642 (30 August 2026)}
}

% Repository owner on GitHub: domino14 (no other contributors listed). Formalises A. Fauzan, "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         = {Source of the port of the prime number theorem used here
                  (commit 3da8eb1b91f9a90a1c0b7959e845c060dbd16256, 23 September 2026)}
}

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

% Repository README (preprints/Catalans-constant-is-irrational-September-24-2026/README.md): "Author: OpenAI",
% "OpenAI Math Release preprint"; produced by an internal model, not peer reviewed. The Lean scope note is
% lean/docs/005.md -> lean/ComparatorChallenges/Catalan.lean (checked to exist on 2026-10-16; not checked by us).
@misc{OpenAICatalan2026,
  author       = {{OpenAI}},
  title        = {Catalan's constant is irrational},
  howpublished = {OpenAI Math Release preprint, \url{https://github.com/openai/math}, file
                  \texttt{preprints/Catalans-constant-is-irrational-September-24-2026/paper.pdf}},
  year         = {2026},
  note         = {September 24, 2026. AI-generated and not peer reviewed; Lean formalisation described in
                  \texttt{lean/docs/005.md} of the same repository}
}