Catalan Constant: source and evidence

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1 \renewcommand{\bibname}{Primary sources}
2 \begin{thebibliography}{9}
3 \addcontentsline{toc}{chapter}{Primary sources}
4 \bibitem{Zudilin2003}
5 Wadim Zudilin.
6 \emph{An Ap\'ery-like difference equation for Catalan's constant}.
7 Electronic Journal of Combinatorics 10(1), R14, 2003.
8 DOI \href{https://doi.org/10.37236/1707}{10.37236/1707}.
9 Checked preprint \href{https://arxiv.org/abs/math/0201024v3}{math/0201024v3}, revised 28 October 2002.
10 Recurrence, limit identification and asymptotic rates. The printed integral prefactor is discussed explicitly in this edition.
11 
12 \bibitem{Zudilin2002}
13 Wadim Zudilin.
14 \emph{A few remarks on linear forms involving Catalan's constant}.
15 Chebyshev Sbornik 3:2(4), 60--70, 2002.
16 Checked \href{https://arxiv.org/abs/math/0210423v1}{math/0210423v1}, 21 October 2002.
17 Asymptotic denominator bounds, distinct from the later sharp bounds.
18 
19 \bibitem{KR2008}
20 Christian Krattenthaler and Tanguy Rivoal.
21 \emph{On a linear form for Catalan's constant}.
22 South East Asian Journal of Mathematics and Mathematical Sciences 6(2), 3--15, 2008.
23 Checked \href{https://arxiv.org/abs/0810.1927v1}{0810.1927v1}, 10 October 2008.
24 Coefficient formula and exact denominator theorems.
25 
26 \bibitem{Zudilin2019}
27 Wadim Zudilin.
28 \emph{Arithmetic of Catalan's constant and its relatives}.
29 Abhandlungen aus dem Mathematischen Seminar der Universit\"at Hamburg 89(1), 45--53, 2019.
30 DOI \href{https://doi.org/10.1007/s12188-019-00203-w}{10.1007/s12188-019-00203-w}.
31 Checked \href{https://arxiv.org/abs/1804.09922v2}{1804.09922v2}, updated 31 May 2019.
32 A disjunction about six even beta values, without isolating Catalan's constant.
33 
34 \bibitem{Eskandari2026}
35 Payman Eskandari.
36 \emph{Improved rational approximations to Catalan's constant}.
37 Preprint \href{https://arxiv.org/abs/2609.26354v1}{2609.26354v1}, 22 September 2026.
38 Integral filter and a guaranteed approximation exponent at least $0.62$, below the irrationality threshold.
39 
40 \bibitem{Sun2026}
41 Zhi-Wei Sun.
42 \emph{Catalan's constant is irrational}.
43 Preprint \href{https://arxiv.org/abs/2609.04176v1}{2609.04176v1}, 3 September 2026.
44 A claimed proof, not imported here as an established theorem.
45 
46 \bibitem{Wachs2026}
47 Dane Wachs.
48 \emph{A note on a recent claimed proof of the irrationality of Catalan's constant}.
49 Preprint \href{https://arxiv.org/abs/2609.22339v1}{2609.22339v1}, 16 September 2026.
50 A criticism of a specified derivation. No rationality conclusion is inferred.
51 \bibitem{Zagier1997}
52 Don Zagier.
53 \emph{Newman's short proof of the prime number theorem}.
54 American Mathematical Monthly 104(8), 705--708, 1997.
55 DOI \href{https://doi.org/10.2307/2975232}{10.2307/2975232}.
56 \href{https://people.mpim-bonn.mpg.de/zagier/files/doi/10.2307/2975232/fulltext.pdf}{Author hosted primary PDF}.
57 The classical input for least common multiple growth.
58 
59 \end{thebibliography}

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