Montgomery,s Pair Correlation Conjecture
المؤلف:
Borwein, J. and Bailey, D
المصدر:
athematics by Experiment: Plausible Reasoning in the 21st Century. Wellesley, MA: A K Peters, 2003.
الجزء والصفحة:
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4-3-2019
1888
Montgomery's Pair Correlation Conjecture
Montgomery's pair correlation conjecture, published in 1973, asserts that the two-point correlation function 
for the zeros of the Riemann zeta function 
on the critical line is
As first noted by Dyson, this is precisely the form expected for the pair correlation of random Hermitian matrices (Derbyshire 2004, pp. 287-291).
REFERENCES:
Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Wellesley, MA: A K Peters, 2003.
Conrey, J. B. "The Riemann Hypothesis." Not. Amer. Math. Soc. 50, 341-353, 2003. http://www.ams.org/notices/200303/fea-conrey-web.pdf.
Derbyshire, J. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. New York: Penguin, 2004.
Sabbagh, K. Dr. Riemann's Zeros: The Search for the $1 Million Solution to the Greatest Problem in Mathematics. Atlantic Books, pp. 134-136, 2002.
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