TOPICS
Search

Montgomery's Pair Correlation Conjecture

Montgomery's pair correlation conjecture, published in 1973, asserts that the two-point correlation function R_2(r) for the zeros of the Riemann zeta function zeta(z) on the critical line is

R_2(r)=1-(sin^2(pir))/((pir)^2).

As first noted by Dyson, this is precisely the form expected for the pair correlation of random Hermitian matrices (Derbyshire 2004, pp. 287-291).

See also

Hilbert-Pólya Conjecture, Montgomery-Odlyzko Law, Riemann Zeta Function, Riemann Zeta Function Zeros

Explore with Wolfram|Alpha

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.

Referenced on Wolfram|Alpha

Montgomery's Pair Correlation Conjecture

Cite this as:

Weisstein, Eric W. "Montgomery's Pair Correlation Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MontgomerysPairCorrelationConjecture.html

Subject classifications