Hafner-Sarnak-McCurley Constant
N.B. A detailed on-line essay by S. Finchwas the starting point for this entry.
Given two randomly chosen Integer 
matrices, what is the probability 
that the correspondingdeterminants are coprime? Hafner et al. (1993) showed that
 | (1) |
is just the probability that two random Integers are coprime, | (2) |
 | (3) |
(Flajolet and Vardi 1996).
References
Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/hafner/hafner.html Flajolet, P. and Vardi, I. ``Zeta Function Expansions of Classical Constants.'' Unpublished manuscript. 1996. http://pauillac.inria.fr/algo/flajolet/Publications/landau.ps. Hafner, J. L.; Sarnak, P.; and McCurley, K. ``Relatively Prime Values of Polynomials.'' In Contemporary Mathematics Vol. 143 (Ed. M. Knopp and M. Seingorn). Providence, RI: Amer. Math. Soc., 1993. Vardi, I. Computational Recreations in Mathematica. Redwood City, CA: Addison-Wesley, 1991.
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