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.