Correlations of eigenvalues and riemann zeros

Communications in Number Theory and Physics

Volumn 2, Issue 3, 2008, Pages 477-536

  Conrey, John Brian ^a   Snaith, Nina Claire ^b  

^a AMERICAN INSTITUTE OF MATHEMATICS   (United States)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70449611028     PISSN: 19314523     EISSN: 19314531     Source Type: Journal    
DOI: 10.4310/CNTP.2008.v2.n3.a1     Document Type: Article

References (21)

1. E.B. Bogomolny and J.P. Keating, Gutzwiller's trace formula and spectral statistics: beyond the diagonal approximation, Phys. Rev. Lett. 77(8) (1996), 1472-1475.
2. E.B. Bogomolny, Random matrix theory and the Riemann zeros II:n-point correlations, Nonlinearity 9 (1996), 911-935.
3. D. Bump and A. Gamburd, On the averages of characteristic polynomials from classical groups, Commun. Math. Phys. 265(1) (2006), 227-274; arXiv:math-ph/0502043.
4. J.B. Conrey, Notes on eigenvalue distributions for the classical compact groups, in Recent Perspectives on Random Matrix Theory and Number Theory, LMS Lecture Note Series, 322, Cambridge University Press, Cambridge, 2005, 111-45.
5. J.B. Conrey, D.W. Farmer, J.P. Keating, M.O. Rubinstein and N.C. Snaith, Integral moments of L-functions, Proc. Lond. Math. Soc. 91(1) (2005), 33-104; arXiv:math.nt/0206018.
6. J.B. Conrey, D.W. Farmer and M.R. Zirnbauer, Autocorrelation of ratios of L-functions, Preprint, arXiv:0711.0718.
7. J.B. Conrey, Howe pairs, supersymmetry, and ratios of random characteristic polynomials for the unitary groups U(N), Preprint, arXiv:mathph/ 0511024.
8. J.B. Conrey, P.J. Forrester and N.C. Snaith, Averages of ratios of characteristic polynomials for the compact classical groups, Int. Math. Res. Not. 7 (2005), 397-431.
9. J.B. Conrey and N.C. Snaith, Triple correlation of the Riemann zeros, to be published in JNTB, arXiv:math/0610495.
10. J.B. Conrey, Applications of the L-functions ratios conjectures, Proc. Lon. Math. Soc. 94(3) (2007), 594-646; arXiv:math.NT/0509480.
11. H. Davenport, Multiplicative number theory, 3rd edn, Springer-Verlag, New York, 2000.
12. F.J. Dyson, Statistical theory of the energy levels of complex systems, i, ii and iii, J. Math. Phys. 3 (1962), 140-175.
13. H.M. Edwards, Riemann's zeta function, Dover Publications, Inc.
14. P. Gao, n-level density of the low-lying zeros of quadratic Dirichlet L-functions, PhD thesis, University of Michigan, 2005.
15. C.P. Hughes and S.J. Miller, Low-lying zeros of L-functions with orthogonal symmetry, Duke Math. J. 136(1) (2007), 115-172.
16. S.G. Krantz, Function theory of several complex variables, 2nd edn, American Mathematical Society, Providence, Rhode Island, 1992.
17. H.L. Montgomery, The pair correlation of the zeta function, Proc. Symp. Pure Math. 24 (1973), 181-93.
18. 20th zero of the Riemann zeta function and 70 million of its neighbors, Preprint, 1989, http://www.dtc.umn.edu/ odlyzko/unpublished/index.html.
19. M.O. Rubinstein, Low-lying zeros of L-functions and random matrix theory, Duke Math. J. 109(1) (2001), 147-181.
20. Z. Rudnick and P. Sarnak, Zeros of principal L-functions and random matrix theory, Duke Math. J. 81(2) (1996), 269-322.
21. E.C. Titchmarsh, The theory of the Riemann zeta function, 2nd edn, Clarendon Press, Oxford, 1986.