Triple correlation of the Riemann zeros
J. Brian Conrey[1]; Nina C. Snaith[2]
- [1] American Institute of Mathematics 360 Portage Ave Palo Alto, CA 94306 School of Mathematics University of Bristol Bristol, BS8 1TW, United Kingdom
- [2] School of Mathematics University of Bristol Bristol, BS8 1TW, United Kingdom
Journal de Théorie des Nombres de Bordeaux (2008)
- Volume: 20, Issue: 1, page 61-106
- ISSN: 1246-7405
Access Full Article
topAbstract
topHow to cite
topReferences
top- M.V. Berry, Semiclassical formula for the number variance of the Riemann zeros. Nonlinearity 1 (1988), 399–407. Zbl0664.10022MR955621
- M.V. Berry, J.P. Keating, The Riemann zeros and eigenvalue asymptotics. SIAM Rev. 41(2) (1999), 236–266. Zbl0928.11036MR1684543
- E.B. Bogomolny, Spectral statistics and periodic orbits. In New Directions in Quantum Chaos; editors, G. Casati, I. Guarneri, and U. Smilansky, pages 333–369. IOS Press, Amsterdam, 2000. Zbl1001.81027MR1843514
- E.B. Bogomolny, J.P. Keating, private communication.
- E.B. Bogomolny, J.P. Keating, Random matrix theory and the Riemann zeros I: three- and four-point correlations. Nonlinearity 8 (1995), 1115–1131. Zbl0834.60105MR1363402
- E.B. Bogomolny, J.P. Keating, Gutzwiller’s trace formula and spectral statistics: beyond the diagonal approximation. Phys. Rev. Lett. 77(8) (1996), 1472–1475. Zbl1182.81034
- E.B. Bogomolny, J.P. Keating, Random matrix theory and the Riemann zeros II:-point correlations. Nonlinearity 9 (1996), 911–935. Zbl0898.60107MR1399479
- J.B. Conrey, -functions and random matrices. In Mathematics Unlimited 2001 and Beyond; editors, B. Enquist and W. Schmid, pages 331–352. Springer-Verlag, Berlin, 2001. arXiv:math.nt/0005300. Zbl1048.11071MR1852163
- 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, pages 111–45. Cambridge University Press, Cambridge, 2005. Zbl1204.11142MR2166460
- J.B. Conrey, D.W. Farmer, J.P. Keating, M.O. Rubinstein, N.C. Snaith, Integral moments of -functions. Proc. Lond. Math. Soc. 91 No. 1 (2005), pages 33–104. arXiv:math.nt/0206018. Zbl1075.11058MR2149530
- J.B. Conrey, D.W. Farmer, M.R. Zirnbauer, Autocorrelation of ratios of characteristic polynomials and of -functions. arXiv:0711.0718. Zbl1178.11056
- J.B. Conrey, D.W. Farmer, M.R. Zirnbauer, Howe pairs, supersymmetry, and ratios of random characteristic polynomials for the unitary groups . Preprint. arXiv:math-ph/0511024.
- J.B. Conrey, P.J. Forrester, N.C. Snaith, Averages of ratios of characteristic polynomials for the compact classical groups. Int. Math. Res. Notices 7 (2005), 397–431. Zbl1156.11334MR2130839
- J.B. Conrey, N.C. Snaith, Applications of the -functions ratios conjectures. Proc. Lon. Math. Soc. 94(3) (2007), 594–646. arXiv:math.NT/0509480. Zbl1183.11050MR2325314
- J.B. Conrey, N.C.Snaith, Correlations of eigenvalues and Riemann zeros. Preprint. arXiv:0803.2795. Zbl1169.11035
- G.H. Hardy, J.E. Littlewood, Contributions to the theory of the Riemann zeta-function and the theory of the distribution of primes. Acta Mathematica 41 (1918), 119–196. Zbl46.0498.01MR1555148
- D.A. Hejhal, On the triple correlation of zeros of the zeta function. Inter. Math. Res. Notices 7 (1994), 293–302. Zbl0813.11048MR1283025
- J.P. Keating, The Riemann zeta function and quantum chaology. In Quantum Chaos; editors, G. Casati, I Guarneri, and U. Smilansky, pages 145–85. North-Holland, Amsterdam, 1993. MR1246830
- J.P. Keating, Periodic orbits, spectral statistics, and the Riemann zeros. In Supersymmetry and trace formulae: chaos and disorder; editors, I.V. Lerner, J.P. Keating, and D.E. Khmelnitskii, pages 1–15. Plenum, New York, 1999.
- J.P. Keating, N.C. Snaith, Random matrix theory and . Commun. Math. Phys. 214 (200), 57–89. Zbl1051.11048MR1794265
- J.P. Keating, N.C. Snaith, Random matrices and -functions. J. Phys. A 36(12) (2003), 2859–81. Zbl1074.11053MR1986396
- M.L. Mehta, Random Matrices. Academic Press, London, second edition, 1991. Zbl0780.60014MR1083764
- H.L. Montgomery, The pair correlation of the zeta function. Proc. Symp. Pure Math 24 (1973), 181–93. Zbl0268.10023MR337821
- Z. Rudnick, P. Sarnak, Zeros of principal -functions and random matrix theory. Duke Mathematical Journal 81(2) (1996), 269–322. Zbl0866.11050MR1395406