Linear statistics of low-lying zeros of L-functions

Quarterly Journal of Mathematics

Volumn 54, Issue 3, 2003, Pages 309-333

  Hughes, C P ^a,b   Rudnick, Z ^a  

^a TEL AVIV UNIVERSITY   (Israel)

^b AMERICAN INSTITUTE OF MATHEMATICS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0142026313     PISSN: 00335606     EISSN: None     Source Type: Journal    
DOI: 10.1093/qmath/hag021     Document Type: Article

References (22)

1. J. B. Conrey and H. Iwaniec, Spacing of zeros of Hecke L-functions and the class number problem, Acta Arith. 103 (2002), 259-312.
2. J. B. Conrey, A. Ghosh, and S. M. Gonek, A note on gaps between zeros of the zeta function, Bull. London Math. Soc. 16 (1984), 421-424.
3. J. B. Conrey, A. Ghosh, D. Goldston, S. M. Gonek, and D. R. Heath-Brown, On the distribution of gaps between zeros of the zeta-function, Quart. J. Math. Oxford 36 (1985), 43-51.
4. P. Diaconis and S. N. Evans, Linear functional of eigenvalues of random matrices, Trans. Amer. Math. Soc. 353 (2001), 2615-2633.
5. P. Diaconis and M. Shahshahani, On the eigenvalues of random matrices, J. Appl. Probab. A 31 (1994), 49-62.
6. F. Haake, M. Kús, H.-J. Sommers, H. Schomerus and K. Życzkowski, Secular determinants of random unitary matrices, J. Phys. A 29 (1996), 3641-3658.
7. C. P. Hughes and Z. Rudnick, Linear statistics for zeros of Riemann's zeta function, C. R. Acad. Sci. Paris, Ser. I 335 (2002), 667-670.
8. C. P. Hughes and Z. Rudnick, Mock-Gaussian behaviour for linear statistics of classical compact groups, J. Phys. A: Math. Gen. 36 (2003), 2919-2932.
9. H. Iwaniec, W. Luo, and P. Sarnak, Low lying zeros of families of L-functions, Publications Mathématiques 91, Institut de Hautes Études Scientifiques, 2000, 55-131.
10. N. M. Katz and P. Sarnak, Random Matrices, Frobenius Eigenvalues, and Monodromy, Colloquium Publications, American Mathematical Society, Providence, 1999.
11. H. L. Montgomery, The pair correlation of zeros of the zeta function, Proceedings of Symposium in Pure Mathematics 24, American Mathematical Society, Providence, 1973, 181-193.
12. H. L. Montgomery and A. M. Odlyzko, Gaps between zeros of the zeta function, Topics in Classical Number Theory, Colloq. Math. Soc. Janos Bolyai 34 (1984), 1079-1106.
13. H. L. Montgomery and R. C. Vaughan, The large sieve, Mathematika 20 (1973), 119-134.
14. A. Özlück, On the q-analogue of the pair correlation conjecture, J. Number Theory 59 (1996), 319-351.
15. A. Özlück and C. Snyder, On the distribution of the non-trivial zeros of quadratic L-functions close to the real axis, Acta Arith. 91 (1999), 209-228.
16. E. Rains, High powers of random elements of compact Lie groups, Probab. Theor. Rel. Fields 107 (1997), 219-241.
17. M. Rubinstein, Low-lying zeros of L-functions and random matrix theory, Duke Math. J. 109 (2001), 147-181.
18. A. Selberg, Contributions to the theory of Dirichlet's L-functions, Skr. Norske Vid. Akad. Oslo. I (1946), 1-62.
19. C. L. Siegel, The zeros of Dirichlet L-functions, Ann. of Math. 46 (1945), 409-422.
20. K. Soundararajan, On the distribution of gaps between zeros of the Riemann zeta-function, Quart. J. Math. Oxford 47 (1996), 383-387.
21. A. Soshnikov, Central limit theorem for local linear statistics in classical compact groups and related combinatorial identities, Ann. Probab. 28 (2000), 1353-1370.
22. E. C. Titchmarch, The zeros of Dirichlet's L-functions, Proc. London Math. Soc. 32 (1931), 488-500.