Low lying zeros of families of L -functions
Publications Mathématiques de l'IHÉS, Volume 91  (2000), p. 55-131
@article{PMIHES_2000__91__55_0,
     author = {Iwaniec, Henryk and Luo, Wenzhi and Sarnak, Peter},
     title = {Low lying zeros of families of $L$-functions},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {91},
     year = {2000},
     pages = {55-131},
     zbl = {01656533},
     mrnumber = {2002h:11081},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_2000__91__55_0}
}
Iwaniec, Henryk; Luo, Wenzhi; Sarnak, Peter. Low lying zeros of families of $L$-functions. Publications Mathématiques de l'IHÉS, Volume 91 (2000) , pp. 55-131. http://www.numdam.org/item/PMIHES_2000__91__55_0/

[AL] A. Atkin and J. Lehner, Hecke operators on Γ(m), Math. Ann. 185 (1970), 134-160. | MR 42 #3022 | Zbl 0177.34901

[AU] A. Abbes and E. Ullmo, Comparison des métriques d'Arakelov et de Poincaré sur X0(N), Duke Math. J. 80 (2) (1995), 295-307. | MR 96k:11077 | Zbl 0895.14007

[CI] B. Conrey and H. Iwaniec, The cubic moment of central values of automorphic L-functions, Ann. of Math., 151 (2000), 1175-1216. | MR 2001g:11070 | Zbl 0973.11056

[De1] P. Deligne, La conjecture de Weil. I, II, Publ. Math. IHES, 48 (1974), 273-308 ; 52 (1981), 313-428. | Numdam

[DFI] W. Duke, J. Friedlander and H. Iwaniec, Class group L-functions, Duke Math. J. 79 (1995), 1-56. | MR 97h:11138 | Zbl 0838.11058

[Fuj] A. Fujii, Some observations concerning the distribution of zeros of zeta functions II, Comment. Math. Univ. St. Pauli 40 (1991), 125-231. | MR 93d:11091 | Zbl 0743.11043

[Gal] P. X. Gallagher, Pair correlation of zeros of the zeta function, J. Reine Angew. Math. 362 (1985), 72-86. | MR 87e:11101 | Zbl 0565.10033

[GJ] S. Gelbart and H. Jacquet, A relation between automorphic representations of GL(2) and GL(3), Ann. Sci. Ecole Norm. Sup. 11 (1978), 411-542. | Numdam | MR 81e:10025 | Zbl 0406.10022

[GR] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, New York, Academic Press, 1965. | MR 33 #5952

[Hej] D. Hejhal, On the triple correlation of the zeros of the zeta-function, IMRN (1994), 293-302. | MR 96d:11093 | Zbl 0813.11048

[HL] J. Hoffstein and P. Lockhart, Coefficients of Maass forms and the Siegel zero; Appendix by D. Goldfeld, J. Hoffstein and D. Lieman, An effective zero-free region, Ann. of Math. 140 (1994), 161-176-181. | MR 95m:11048 | Zbl 0814.11032

[Iwa] H. Iwaniec, Topics in classical automorphic forms, Grad. Studies in Math., (17) AMS (1997). | MR 98e:11051 | Zbl 0905.11023

[IS] H. Iwaniec and P. Sarnak, The non-vanishing of central values of automorphic L-functions and Landau-Siegel zeros, Israel Math. J., to appear. | Zbl 0992.11037

[JP-SS] H. Jacquet, I. Piatetski-Shapiro, J. Shalika, Rankin-Selberg convolutions, Amer. J. Math. 105 (1983), 367-464. | MR 85g:11044 | Zbl 0525.22018

[KS1] N. Katz and P. Sarnak, Random Matrices, Frobenius Eigenvalues and Monodromy, AMS Colloq. Publ. 45 (1999). | MR 2000b:11070 | Zbl 0958.11004

[KS2] N. Katz and P. Sarnak, Zeros of zeta functions and symmetry, Bull. AMS 36 (1999), 1-26. | MR 2000f:11114 | Zbl 0921.11047

[KM1] E. Kowalski and P. Michel, The analytic rank of J0(q) and zeros of automorphic L-functions, Duke Math. J. 100 (1999), 503-547. | MR 2001b:11060 | Zbl 01425264

[KM2] E. Kowalski and P. Michel, A lower bound for the rank of J0(q), Acta Arith., 94 (2000), 303-343. | MR 2003a:11054 | Zbl 0973.11065

[KMV1] E. Kowalski, P. Michel and J. Vanderkam, Non-vanishing of high derivatives of automorphic L-functions at the center of the critical strip, J. Reine Angew. Math., 526 (2000), 1-34. | MR 2001h:11068 | Zbl 1020.11033

[KMV2] E. Kowalski, P. Michel and J. Vanderkam, Mollification of the fourth moment of automorphic L-functions and arithmetic applications, Invent. Math. 142 (2000), 95-151. | MR 2001m:11080 | Zbl 1054.11026

[KMV3] E. Kowalski, P. Michel and J. Vanderkam, Rankin-Selberg L-functions in the level aspect, Preprint (2000). | Zbl 01820921

[LW] S. Lang and A. Weil, Number of points of varieties in finite fields, Amer. J. Math. 76 (1954), 819-827. | MR 16,398d | Zbl 0058.27202

[Li] W. Li, Newforms and functional equations, Math. Ann. 212 (1975), 285-315. | MR 51 #5498 | Zbl 0278.10026

[Miy] T. Miyake, Modular Forms, Springer-Verlag, 1989. | MR 90m:11062 | Zbl 0701.11014

[Mon] H. L. Montgomery, The pair correlation of zeros of the zeta-function, Proc. Symp. Pure Math. AMS 24 (1973), 181-193. | MR 49 #2590 | Zbl 0268.10023

[P1] H. Petersson, Zur analytischen Theorie der Grenzkreisgruppen. I-V, Math. Ann. 115 (1938), 23-61 ; 175-204 ; 518-512 ; 670-709 ; Math. Z. 44 (1938), 127-155. | JFM 64.1076.01 | Zbl 0019.02202

[P2] H. Petersson, Über die Entwicklungskoefficienten der automorphen formen, Acta Math. 58 (1932), 169-215. | JFM 58.1110.01 | Zbl 0003.35002

[R] M. Rubinstein, private communication, 1998.

[RS] Z. Rudnick and P. Sarnak, Principal L-functions and random matrix theory, Duke Math. J. 81 (2) (1996), 269-322. | MR 97f:11074 | Zbl 0866.11050

[S1] G. Shimura, On the holomorphy of certain Dirichlet series, Proc. London Math. Soc. 31 (3) (1975), 79-98. | MR 52 #3064 | Zbl 0311.10029

[S2] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton, NJ, Princeton University Press, 1971. | Zbl 0221.10029

[Tit] E. C. Titchmarsh, The Theory of the Riemann Zeta-function, Oxford (second edition), Clarendon Press, 1986. | MR 88c:11049 | Zbl 0601.10026

[Van] J. Vanderkam, The rank of quotients of J0(N), Duke Math. J. 97 (3) (1999), 545-577. | MR 2000i:11103 | Zbl 1013.11030

[Vin] I. M. Vinogradov, Estimate of a prime-number trigonometric sum (in Russian), Izv. Akad. Nauk SSSR Ser. Mat. 23 (1959), 157-164 ; Special Variants of the Method of Trigonometric Sums, Selected Works, Springer-Verlag, 1984. | MR 21 #5611 | Zbl 0088.03902

[Wat] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, 1944. | MR 6,64a | Zbl 0063.08184