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| The '''Hafner–Sarnak–McCurley constant''' is a [[mathematical constant]] representing the [[probability]] that the [[matrix determinant|determinants]] of two randomly chosen square [[integer matrix|integer matrices]] will be [[relatively prime]]. The probability depends on the matrix size, ''n'', in accordance with the formula | | The writer is known by the name of Figures Lint. Managing individuals has been his day job for a while. California is where her house is but she requirements to move because of her family. One of the extremely best things in the globe for him is to collect badges but he is struggling to discover time for it.<br><br>Also visit my web page; [http://dore.gia.ncnu.edu.tw/88ipart/node/1326254 dore.gia.ncnu.edu.tw] |
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| :<math>D(n)=\Pi_{k=1}^{\infty}\left\{1-[1-\Pi_{j=1}^n(1-p_k^{-j})]^2\right\},</math>
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| where ''p<sub>k</sub>'' is the ''k''th prime number. The constant is the limit of this expression as ''n'' approaches infinity. Its value is roughly 0.3532363719... {{OEIS|A085849}}; Ilan Vardi has given it the alternate expression
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| :<math>\Pi_{k=2}^{\infty}{\zeta(k) ^{-a_k}},</math>
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| which converges exponentially; here ζ(''k'') is the [[Riemann zeta function]]. <!-- How are the a_k's determined? -->
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| ==References==
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| *{{Citation |last=Finch |first=S. R. |chapter=§2.5 Hafner-Sarnak-McCurley Constant |title=Mathematical Constants |location=Cambridge, England |publisher=Cambridge University Press |pages=110–112 |year=2003 |isbn=0-521-81805-2 }}.
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| *{{Citation |last=Flajolet |first=P. |lastauthoramp=yes |last2=Vardi |first=I. |title=Zeta Function Expansions of Classical Constants |work=Unpublished manuscript |year=1996 |url=http://algo.inria.fr/flajolet/Publications/landau.ps }}.
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| *{{Citation |last=Hafner |first=J. L. |authorlink2=Peter Sarnak |last2=Sarnak |first2=P. |lastauthoramp=yes |authorlink3=Kevin McCurley (cryptographer) |last3=McCurley |first3=K. |chapter=Relatively Prime Values of Polynomials |title=A Tribute to Emil Grosswald: Number Theory and Related Analysis |editor1-first=M. |editor1-last=Knopp |editor2-first=M. |editor2-last=Seingorn |location=Providence, RI |publisher=Amer. Math. Soc. |year=1993 |isbn=0-8218-5155-1 }}.
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| *{{Citation |last=Vardi |first=I. |title=Computational Recreations in Mathematica |location=Redwood City, CA |publisher=Addison-Wesley |year=1991 |isbn=0-201-52989-0 }}.
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| ==External links==
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| * {{MathWorld|urlname=Hafner-Sarnak-McCurleyConstant|title=Hafner-Sarnak-McCurley Constant}}
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| {{DEFAULTSORT:Hafner-Sarnak-McCurley constant}}
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| [[Category:Mathematical constants]]
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Revision as of 16:20, 4 March 2014
The writer is known by the name of Figures Lint. Managing individuals has been his day job for a while. California is where her house is but she requirements to move because of her family. One of the extremely best things in the globe for him is to collect badges but he is struggling to discover time for it.
Also visit my web page; dore.gia.ncnu.edu.tw