Répartition des zéros des fonctions $L$ et matrices aléatoires

Michel, Philippe

Séminaire Bourbaki : volume 2000/2001, exposés 880-893, Astérisque, no. 282 (2002), Exposé no. 887, 38 p.

[B] E. Bombieri - A lower bound for the zeros of Riemann's zeta function on the critical line (following N. Levinson). Séminaire Bourbaki, Exp. n° 465, Lecture Notes in Math. 514 (1976), 176-182. | Numdam | Zbl | MR

[BH] E. Brézin, S. Hikami - Characteristic polynomials of random matrices. Comm. Math. Phys. 214, no. 1 (2000), 111-135. | Zbl | MR

[Br] A. Brumer - The rank of J0(N), Columbia University Number Theory Seminar (New York, 1992), Astérisque 228, 3 (1995), 41-68. | Zbl | MR

[Co] A. Connes - Trace formula in noncommutative geometry and the zeros of the Riemann zeta function. Selecta Math. (N.S.) 5, no. 1 (1999), 29-106. | Zbl | MR

[CF] J. B. Conrey, D. W. Farmer - Mean values of L-functions and symmetry, Internat. Math. Res. Notices 17 (2000), 883-908. | Zbl | MR

[CG] J. B. Conrey, A. Ghosh - A conjecture for the sixth power moment of the Riemann zeta-function, Internat. Math. Res. Notices 15 (1998), 775-780. | Zbl | MR

[CI1] B. Conrey, H. Iwaniec - The cubic moment of central values of automorphic L-functions Ann. Math, 151, no. 3 (2000), 1175-1216 . | Zbl | MR

[CI2] B. Conrey, H. Iwaniec - Spacing of zeros of Hecke L-functions and the class number problem. Acta Arith. 103, no. 3 (2002), 259-312. | Zbl | MR

[CKRS] J. B. Conrey, J. P. Keating, M. Rubinstein, N. C. Snaith - On the frequency of vanishing of quadratic twists of modular L-functions. Preprint (2000). | MR

[CS] J. B. Conrey, K. Soundararajan - Real zeros of quadratic Dirichlet L-functions. Invent. Math. 150, no. 1 (2002), 1-44. | Zbl | MR

[De1] P. Deligne - La conjecture de Weil, I, Publ. Math. IHES 43 (1974), 273- 308. | Numdam | Zbl | MR

[De2] P. Deligne - La conjecture de Weil, II, Publ. Math. IHES 52 (1980), 137- 252. | Numdam | Zbl | MR

[Du] W. Duke - The critical order of vanishing of automorphic L-functions with high level, Invent. Math. 119 (1995), 165-174. | Zbl | MR

[DFI1] W. Duke, J. Friedlander, H. Iwaniec - Bounds for automorphic L-functions. Invent. Math. 112, no. 1 (1993), 1-8. | Zbl | MR

[DFI2] W. Duke, J. Friedlander, H. Iwaniec - Bounds for automorphic L-functions. II, Invent. Math. 115 (1994). | Zbl | MR

[DFI3] W. Duke, J. Friedlander, H. Iwaniec - Class group L-functions. Duke Math. J. 79, no. 1 (1995), 1-56. | Zbl | MR

[DFI4] W. Duke, J. Friedlander, H. Iwaniec - Bounds for automorphic L-functions. III, Invent. Math. 143, 2 (2001), 221-248. | Zbl | MR

[EMOT] A. Erdeilyi, W. Magnus, F. Oberhettinger, F. G. Tricomi - Higher Transcendental functions, Vol. I, II, III. Based, in part, on notes left by Harry Bateman. McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953. | Zbl | MR

[FI] E. Fouvry, H. Iwaniec - Low lying zeros of dihedral L functions. Preprint. | MR

[GoJ] R. Godement, H. Jacquet - Zeta functions of simple algebras. Lecture Notes in Math. 260 (1972). | Zbl | MR

[GZ] W. Gross, D. Zagier - Heegner points and derivatives of L-series. Invent. Math. 84, no. 2 (1986), 225-320. | Zbl | MR

[HB] D. R. Heath-Brown - The fourth power mean of Dirichlet's L-functions, Analysis 1, no. 1 (1981), 25-32. | Zbl | MR

[HM] D. R. Heath-Brown, P. Michel - Exponential decays for the frequency of the analytic rank of Automorphic L-functions, Duke Math. J. 102, no. 3 (2000), 475-484. | Zbl | MR

[He] S. Helgason - Differential geometry, Lie groups, and symmetric spaces. Pure and Appl. Math. 80, Academic Press (1978). | Zbl | MR

[ILS] H. Iwaniec, W. Luo, P. Sarnak - Low Lying Zeros of families of L-functions, Publ. IHES. 91 (2001), 55-131. | Zbl | MR | Numdam

[IS1] H. Iwaniec, P. Sarnak - The non-vanishing of central values of automorphic L-functions and Siegel-Landau zeros, Israel J. Math. 120, Part A (2000), 155-177. | Zbl | MR

[IS2] H. Iwaniec, P. Sarnak - Perspectives in the Analytic Theory of L functions. Preprint (2000). | MR

[JS] H. Jacquet, J. A. Shalika - On Euler products and the classification of automorphic representations. I, Amer. J. Math. 103, no. 3 (1981), 499-558. | Zbl | MR

[JPPS] H. Jacquet, I. I. Piatetskii-Shapiro, J. A. Shalika - Rankin-Selberg convolutions, Amer. J. Math. 105, no. 2 (1983), 367-464. | Zbl | MR

[Ka] N. M. Katz - Gauss Sums, Kloosterman Sums and Monodromy Groups, Annals of Maths. Studies 116, PUP. | Zbl

[KSa] N. M. Katz, P. Sarnak - Random matrices, Frobenius eigenvalues, and monodromy. American Math. Soc. Colloquium Publications 45 (1999). | Zbl | MR

[KSn1] J. P. Keating, N. C. Snaith - Random matrix theory and L-functions at s = 1/2. Comm. Math. Phys. 214, no. 1 (2000), 91-110. | Zbl | MR

[KSn2] J. P. Keating, N. C. Snaith - Random matrix theory and ζ(1/2 + it). Comm. Math. Phys. 214, no. 1 (2000), 57-89. | Zbl

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

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

[KMV2] E. Kowalski, P. Michel, J. Vanderkam - Mollification of the fourth moment of automorphic L-functions and arithmetic applications, Invent. Math. 142, 1 (2000), 95-151. | Zbl | MR

[KMV3] E. Kowalski, P. Michel, J. Vanderkam - Rankin-Selberg L functions in the level aspect, Duke Math. J. 114, no. 1 (2002), 123-191. | Zbl | MR

[Me] M. L. Mehta - Random matrices. Second edition. Academic Press, Inc., Boston, MA, 1991. | Zbl | MR

[MV] P. Michel, J. Vanderkam - Simultaneous non-vanishing of twists of automorphic L-functions. Preprint 2001.

[Mo] H. L. Montgomery - The pair correlation of zeros of the zeta function. Analytic number theory (Proc. Sympos. Pure Math., Vol. XXIV), (1972), 181-193. | Zbl | MR

[Mu] R. Murty - The analytic rank of J0(N)(Q), Number theory (Halifax, NS, 1994), 263-277, CMS Conf. Proc., 15, Amer. Math. Soc., Providence, RI, 1995. | Zbl | MR

[Od] A. M. Odlyzko - The 1020th zero of the Riemann zeta function and 70 millions of its neighbors. Preprint ATT, 1989.

[OS] A. Ozluk, C. Snider - Small zeros of quadratic L functions, Bull. Aust. Math. Soc. 47 (1993), 307-319. | Zbl | MR

[P] A. Peng - Ph. D. Thesis, Princeton University 2001.

[Ro] E. Royer - Petits zéros de fonctions L de formes modulaires, Acta Arith. 99, no. 2 (2001), 147-172.. | Zbl | MR

[Ru] M. Rubinstein - Evidence for a spectral interpretation of the zéros of L-functions, PhD Thesis, Princeton University, 1998.

[RS] Z. Rudnick, P. Sarnak - Zeros of principal L-functions and random matrix theory, A celebration of John F. Nash, Jr. Duke Math. J. 81, no. 2 (1996), 269-322. | Zbl | MR

[Sa] P. Sarnak - Estimates for Rankin-Selberg L-functions and quantum unique ergodicity, J. Funct. Anal. 184, no. 2 (2001), 419-453. | Zbl | MR

[Se] A. Selberg - Contributions to the theory of Dirichlet's L functions, Skr. utg. av Det Norske Videnskaps-Akademi, Mat. Nat. Kl., No. 3 (1946), 1-62. | Zbl | MR

[So] K. Soundararajan - Non-vanishing of quadratic Dirichlet L-functions at s = 1/2, Ann. of Math. 152, No. 2, 447-488. | Zbl | MR

[Ti] E. C. Titchmarsh - The theory of the Riemann zeta-function. Second edition. Edited and with a preface by D.R. Heath-Brown. The Clarendon Press, Oxford University Press, New York, 1986. | Zbl | MR

[Va] J. Vanderkam - Non-vanishing of Hilbert modular L-functions at the center of the critical strip. Preprint (1998).

[Wa] J.-L. Waldspurger - Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pures et Appl. 60 (1981), 375-484. | Zbl | MR

[Zi] M. Zirnbauer - Riemannian symmetric superspaces and their origin in random-matrix theory. J. Math. Phys. 37, no. 10 (1996), 4986-5018. | Zbl | MR