Low lying zeros of families of L -functions
Publications Mathématiques de l'IHÉS, Tome 91 (2000), pp. 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},
     pages = {55--131},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {91},
     year = {2000},
     mrnumber = {2002h:11081},
     zbl = {01656533},
     language = {en},
     url = {http://archive.numdam.org/item/PMIHES_2000__91__55_0/}
}
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Iwaniec, Henryk; Luo, Wenzhi; Sarnak, Peter. Low lying zeros of families of $L$-functions. Publications Mathématiques de l'IHÉS, Tome 91 (2000), pp. 55-131. http://archive.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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

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

[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 | Zbl

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

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

[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 | Zbl

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

[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

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

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

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

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

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

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

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

[Miy] T. Miyake, Modular Forms, Springer-Verlag, 1989. | MR | Zbl

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

[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 | Zbl

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

[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 | Zbl

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

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

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

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

[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 | Zbl

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