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Decimal expansion of the asymptotic probability that 2 random integer 3 X 3 matrices generate the ring M_3(Z).
1

%I #8 Jan 13 2024 10:44:58

%S 3,0,7,4,5,2,4,6,7,6,8,0,3,6,6,0,5,1,6,3,5,7,9,8,5,4,6,6,2,2,1,1,1,6,

%T 2,9,4,4,4,2,8,8,6,1,1,7,0,0,7,9,4,5,5,5,5,1,3,9,5,1,5,8,2,0,9,4,6,1,

%U 2,6,6,4,3,3,8,5,3,7,6,2,9,4,9,8,8,1,0,1,3,2,5,7,9,3,8,2,9,1,9,7,8,0,7,5,1

%N Decimal expansion of the asymptotic probability that 2 random integer 3 X 3 matrices generate the ring M_3(Z).

%H Steven Finch, <a href="https://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, arXiv:2001.00578 [math.HO], 2020-2022. See p. 40.

%H Rostyslav V. Kravchenko, Marcin Mazur, and Bogdan V. Petrenko, <a href="http://dx.doi.org/10.2140/ant.2012.6.243">On the smallest number of generators and the probability of generating an algebra</a>, Algebra & Number Theory, Vol. 6, No. 2 (2012), pp. 243-291; <a href="https://arxiv.org/abs/1001.2873">arXiv preprint</a>, arXiv:1001.2873 [math.RA], 2010.

%F Equals 1/(zeta(2)^2*zeta(3)).

%e 0.30745246768036605163579854662211162944428861170079...

%t RealDigits[1/(Zeta[2]^2*Zeta[3]), 10, 120][[1]]

%o (PARI) 1/(zeta(2)^2*zeta(3))

%Y Cf. A002117, A013661, A369095.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Jan 13 2024