
@article{RivoalZudilin2003,
  author  = {Rivoal, Tanguy and Zudilin, Wadim},
  title   = {Diophantine properties of numbers related to {Catalan}'s constant},
  journal = {Mathematische Annalen},
  volume  = {326},
  number  = {4},
  pages   = {705--721},
  year    = {2003},
  doi     = {10.1007/s00208-003-0420-2},
  url     = {https://rivoal.perso.math.cnrs.fr/articles/betacatalan.pdf}
}

@article{Zudilin2003,
  author  = {Zudilin, Wadim},
  title   = {An {Ap\'ery}-like difference equation for {Catalan}'s constant},
  journal = {The Electronic Journal of Combinatorics},
  volume  = {10},
  number  = {1},
  pages   = {R14},
  year    = {2003},
  note    = {10 pp.; preprint arXiv:math/0201024v3},
  doi     = {10.37236/1707},
  url     = {https://arxiv.org/abs/math/0201024v3}
}

@article{KrattenthalerZudilin2019,
  author  = {Krattenthaler, Christian and Zudilin, Wadim},
  title   = {Hypergeometry inspired by irrationality questions},
  journal = {Kyushu Journal of Mathematics},
  volume  = {73},
  number  = {1},
  pages   = {189--203},
  year    = {2019},
  doi     = {10.2206/kyushujm.73.189},
  note    = {Preprint arXiv:1802.08856v2},
  url     = {https://arxiv.org/abs/1802.08856v2}
}

@article{Rivoal2006Catalan,
  author  = {Rivoal, Tanguy},
  title   = {Nombres d'{Euler}, approximants de {Pad\'e} et constante de {Catalan}},
  journal = {The Ramanujan Journal},
  volume  = {11},
  number  = {2},
  pages   = {199--214},
  year    = {2006},
  doi     = {10.1007/s11139-006-6507-0},
  url     = {https://rivoal.perso.math.cnrs.fr/articles/gnew6.pdf}
}

@article{KrattenthalerRivoal2008Catalan,
  author  = {Krattenthaler, Christian and Rivoal, Tanguy},
  title   = {On a linear form for {Catalan}'s constant},
  journal = {South East Asian Journal of Mathematics and Mathematical Sciences},
  volume  = {6},
  number  = {2},
  pages   = {3--15},
  year    = {2008},
  note    = {Preprint arXiv:0810.1927v1},
  url     = {https://arxiv.org/abs/0810.1927v1}
}

@misc{Eskandari2026Approximations,
  author       = {Eskandari, Payman},
  title        = {Improved rational approximations to {Catalan}'s constant},
  year         = {2026},
  howpublished = {Preprint, arXiv:2609.26354v1 [math.NT]},
  note         = {Submitted 22 September 2026},
  url          = {https://arxiv.org/abs/2609.26354v1}
}

@article{Zudilin2019,
  author  = {Zudilin, Wadim},
  title   = {Arithmetic of {Catalan}'s constant and its relatives},
  journal = {Abhandlungen aus dem Mathematischen Seminar der Universit{\"a}t Hamburg},
  volume  = {89},
  number  = {1},
  pages   = {45--53},
  year    = {2019},
  doi     = {10.1007/s12188-019-00203-w},
  note    = {Preprint arXiv:1804.09922v2},
  url     = {https://arxiv.org/abs/1804.09922v2}
}

@article{Zagier1997,
  author  = {Zagier, Don},
  title   = {{Newman}'s short proof of the prime number theorem},
  journal = {The American Mathematical Monthly},
  volume  = {104},
  number  = {8},
  pages   = {705--708},
  year    = {1997},
  doi     = {10.2307/2975232},
  url     = {https://people.mpim-bonn.mpg.de/zagier/files/doi/10.2307/2975232/fulltext.pdf}
}

@misc{Sun2026,
  author        = {Sun, Zhi-Wei},
  title         = {{Catalan}'s constant is irrational},
  year          = {2026},
  howpublished  = {Preprint, arXiv:2609.04176v1 [math.GM]},
  note          = {Submitted 3 September 2026},
  url           = {https://arxiv.org/abs/2609.04176v1}
}

@incollection{Apery1979,
  author = {Ap{\'e}ry, Roger},
  title = {Irrationalit{\'e} de $\zeta 2$ et $\zeta 3$},
  booktitle = {Journ{\'e}es Arithm{\'e}tiques de Luminy},
  series = {Ast{\'e}risque},
  number = {61},
  pages = {11--13},
  year = {1979},
  publisher = {Soci{\'e}t{\'e} math{\'e}matique de France},
  url = {https://numdam.org/item/AST_1979__61__11_0/}
}

@article{Beukers1979,
  author = {Beukers, Frits},
  title = {A note on the irrationality of {$\zeta(2)$} and {$\zeta(3)$}},
  journal = {Bulletin of the London Mathematical Society},
  volume = {11},
  number = {3},
  pages = {268--272},
  year = {1979},
  doi = {10.1112/blms/11.3.268},
  url = {https://doi.org/10.1112/blms/11.3.268}
}

@article{LaiZhou2022,
  author = {Lai, Li and Zhou, Li},
  title = {At least two of {$\zeta(5),\zeta(7),\ldots,\zeta(35)$} are irrational},
  journal = {Publicationes Mathematicae Debrecen},
  volume = {101},
  number = {3--4},
  pages = {353--372},
  year = {2022},
  doi = {10.5486/PMD.2022.9252},
  note = {Preprint arXiv:2103.00904v2},
  url = {https://arxiv.org/abs/2103.00904v2}
}

@article{Fischler2020,
  author = {Fischler, St{\'e}phane},
  title = {Irrationality of values of {$L$}-functions of {Dirichlet} characters},
  journal = {Journal of the London Mathematical Society},
  volume = {101},
  number = {2},
  pages = {857--876},
  year = {2020},
  doi = {10.1112/jlms.12290},
  url = {https://www.imo.universite-paris-saclay.fr/~stephane.fischler/Lschi.pdf}
}

@article{Nesterenko2016Catalan,
  author = {Nesterenko, Yu. V.},
  title = {On {Catalan}'s constant},
  journal = {Proceedings of the Steklov Institute of Mathematics},
  volume = {292},
  pages = {153--170},
  year = {2016},
  doi = {10.1134/S0081543816010107},
  url = {https://doi.org/10.1134/S0081543816010107}
}

@article{Viola2022Catalan,
  author = {Viola, Carlo},
  title = {Rational approximations to {Catalan}'s constant},
  journal = {Oberwolfach Reports},
  volume = {19},
  number = {2},
  pages = {1100--1101},
  year = {2022},
  note = {Joint work with Raffaele Marcovecchio; contribution to Report 21/2022,
          Diophantische Approximationen},
  doi = {10.4171/OWR/2022/21},
  url = {https://ems.press/content/serial-article-files/46958}
}

@misc{CalegariDimitrovTang2024,
  author = {Calegari, Frank and Dimitrov, Vesselin and Tang, Yunqing},
  title = {The linear independence of {$1$, $\zeta(2)$, and $L(2,\chi_{-3})$}},
  year = {2024},
  howpublished = {Preprint, arXiv:2408.15403v2},
  note = {Revised 16 September 2024},
  url = {https://arxiv.org/abs/2408.15403v2}
}

@article{Calegari2005,
  author = {Calegari, Frank},
  title = {Irrationality of certain {$p$}-adic periods for small {$p$}},
  journal = {International Mathematics Research Notices},
  volume = {2005},
  number = {20},
  pages = {1235--1249},
  year = {2005},
  doi = {10.1155/IMRN.2005.1235},
  url = {https://www.math.uchicago.edu/~fcale/papers/Beukers.pdf}
}

@misc{CalegariDimitrovTang2025,
  author = {Calegari, Frank and Dimitrov, Vesselin and Tang, Yunqing},
  title = {Arithmetic holonomy bounds and effective {Diophantine} approximation},
  year = {2025},
  howpublished = {Preprint, arXiv:2510.04156v1},
  note = {5 October 2025},
  url = {https://arxiv.org/abs/2510.04156v1}
}

@article{Zudilin2017Determinantal,
  author = {Zudilin, Wadim},
  title = {A determinantal approach to irrationality},
  journal = {Constructive Approximation},
  volume = {45},
  number = {2},
  pages = {301--310},
  year = {2017},
  doi = {10.1007/s00365-016-9333-7},
  note = {Preprint arXiv:1507.05697v2},
  url = {https://arxiv.org/abs/1507.05697v2}
}

@misc{Forrester2018Andreief,
  author = {Forrester, Peter J.},
  title = {Meet {Andr\'eief}, {Bordeaux} 1886, and {Andreev}, {Kharkov} 1882--83},
  year = {2018},
  howpublished = {Preprint, arXiv:1806.10411v1},
  url = {https://arxiv.org/abs/1806.10411v1}
}

@article{Krattenthaler1999,
  author = {Krattenthaler, Christian},
  title = {Advanced determinant calculus},
  journal = {S\'eminaire Lotharingien de Combinatoire},
  volume = {42},
  pages = {B42q},
  year = {1999},
  note = {67 pp.; arXiv:math/9902004v3},
  url = {https://arxiv.org/abs/math/9902004v3}
}

@article{Sarason1967,
  author = {Sarason, Donald},
  title = {Generalized interpolation in {$H^\infty$}},
  journal = {Transactions of the American Mathematical Society},
  volume = {127},
  number = {2},
  pages = {179--203},
  year = {1967},
  doi = {10.1090/S0002-9947-1967-0208383-8},
  url = {https://doi.org/10.1090/S0002-9947-1967-0208383-8}
}

@article{GaroufalidisPopescu2013,
  author = {Garoufalidis, Stavros and Popescu, Ionel},
  title = {Analyticity of the Planar Limit of a Matrix Model},
  journal = {Annales Henri Poincar\'e},
  volume = {14},
  pages = {499--565},
  year = {2013},
  doi = {10.1007/s00023-012-0191-y},
  url = {https://doi.org/10.1007/s00023-012-0191-y}
}

@article{Saff2010,
  author = {Saff, Edward B.},
  title = {Logarithmic Potential Theory with Applications to Approximation Theory},
  journal = {Surveys in Approximation Theory},
  volume = {5},
  pages = {165--200},
  year = {2010},
  note = {arXiv:1010.3760v1},
  url = {https://arxiv.org/abs/1010.3760v1}
}

@misc{DLMFChebyshev,
  author = {{National Institute of Standards and Technology}},
  title = {{Digital Library of Mathematical Functions}, Section 18.5},
  year = {n.d.},
  note = {Equations (18.5.1)--(18.5.2); accessed September 24, 2026},
  url = {https://dlmf.nist.gov/18.5}
}

@incollection{Descartes1637,
  author = {Descartes, Ren{\'e}},
  title = {La G{\'e}om{\'e}trie},
  booktitle = {Discours de la m{\'e}thode},
  publisher = {Jan Maire},
  address = {Leyde},
  year = {1637},
  note = {Book III, p. 373},
  url = {https://www.unicaen.fr/puc/sources/prodescartes/consult/descartes/Oeuvres/Oeuvres_Descartes/discours_de_la_methode.xml/la_geometrie.html}
}

@article{Agol2010TwoCusps,
  author = {Agol, Ian},
  title = {The minimal volume orientable hyperbolic 2-cusped 3-manifolds},
  journal = {Proceedings of the American Mathematical Society},
  volume = {138},
  number = {10},
  pages = {3723--3732},
  year = {2010},
  doi = {10.1090/S0002-9939-10-10364-5},
  note = {Linked preprint arXiv:0804.0043v2, revised 18 May 2010},
  url = {https://arxiv.org/abs/0804.0043v2}
}

@book{Voight2021Quaternion,
  author = {Voight, John},
  title = {Quaternion Algebras},
  series = {Graduate Texts in Mathematics},
  volume = {288},
  publisher = {Springer},
  address = {Cham},
  year = {2021},
  doi = {10.1007/978-3-030-56694-4},
  url = {https://link.springer.com/book/10.1007/978-3-030-56694-4}
}
