where pk is the kth prime number. The constant is the limit of this expression as n approaches infinity. Its value is roughly 0.3532363719... (sequence A085849 in the OEIS).
Referencesedit
Finch, S. R. (2003), "§2.5 Hafner–Sarnak–McCurley Constant", Mathematical Constants, Cambridge, England: Cambridge University Press, pp. 110–112, ISBN0-521-81805-2.
Flajolet, P. & Vardi, I. (1996), "Zeta Function Expansions of Classical Constants", Unpublished manuscript.
Hafner, J. L.; Sarnak, P. & McCurley, K. (1993), "Relatively Prime Values of Polynomials", in Knopp, M. & Seingorn, M. (eds.), A Tribute to Emil Grosswald: Number Theory and Related Analysis, Providence, RI: Amer. Math. Soc., ISBN0-8218-5155-1.
Vardi, I. (1991), Computational Recreations in Mathematica, Redwood City, CA: Addison–Wesley, ISBN0-201-52989-0.
hafner, sarnak, mccurley, constant, mathematical, constant, representing, probability, that, determinants, randomly, chosen, square, integer, matrices, will, relatively, prime, probability, depends, matrix, size, accordance, with, formula, displaystyle, prod, . The Hafner Sarnak McCurley constant is a mathematical constant representing the probability that the determinants of two randomly chosen square integer matrices will be relatively prime The probability depends on the matrix size n in accordance with the formula D n k 1 1 1 j 1 n 1 p k j 2 displaystyle D n prod k 1 infty left 1 left 1 prod j 1 n 1 p k j right 2 right where pk is the kth prime number The constant is the limit of this expression as n approaches infinity Its value is roughly 0 3532363719 sequence A085849 in the OEIS References editFinch S R 2003 2 5 Hafner Sarnak McCurley Constant Mathematical Constants Cambridge England Cambridge University Press pp 110 112 ISBN 0 521 81805 2 Flajolet P amp Vardi I 1996 Zeta Function Expansions of Classical Constants Unpublished manuscript Hafner J L Sarnak P amp McCurley K 1993 Relatively Prime Values of Polynomials in Knopp M amp Seingorn M eds A Tribute to Emil Grosswald Number Theory and Related Analysis Providence RI Amer Math Soc ISBN 0 8218 5155 1 Vardi I 1991 Computational Recreations in Mathematica Redwood City CA Addison Wesley ISBN 0 201 52989 0 External links editWeisstein Eric W Hafner Sarnak McCurley Constant MathWorld nbsp This number theory related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Hafner Sarnak McCurley constant amp oldid 1148442810, wikipedia, wiki, book, books, library,