Répartition des zéros des fonctions et matrices aléatoires
Séminaire Bourbaki (2000-2001)
- Volume: 43, page 211-248
- ISSN: 0303-1179
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topMichel, Philippe. "Répartition des zéros des fonctions $L$ et matrices aléatoires." Séminaire Bourbaki 43 (2000-2001): 211-248. <http://eudml.org/doc/110290>.
@article{Michel2000-2001,
author = {Michel, Philippe},
journal = {Séminaire Bourbaki},
keywords = {-functions; random matrices; zeros},
language = {fre},
pages = {211-248},
publisher = {Société Mathématique de France},
title = {Répartition des zéros des fonctions $L$ et matrices aléatoires},
url = {http://eudml.org/doc/110290},
volume = {43},
year = {2000-2001},
}
TY - JOUR
AU - Michel, Philippe
TI - Répartition des zéros des fonctions $L$ et matrices aléatoires
JO - Séminaire Bourbaki
PY - 2000-2001
PB - Société Mathématique de France
VL - 43
SP - 211
EP - 248
LA - fre
KW - -functions; random matrices; zeros
UR - http://eudml.org/doc/110290
ER -
References
top- [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. Zbl0326.10034MR444585
- [BH] E. Brézin, S. Hikami — Characteristic polynomials of random matrices. Comm. Math. Phys.214, no. 1 (2000), 111-135. Zbl1042.82017MR1794268
- [Br] A. Brumer - The rank of J0(N), Columbia University Number Theory Seminar (New York, 1992), Astérisque228, 3 (1995), 41-68. Zbl0851.11035MR1330927
- [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. Zbl0945.11015MR1694895
- [CF] J.B. Conrey, D.W. Farmer — Mean values of L-functions and symmetry, Internat. Math. Res. Notices17 (2000), 883-908. Zbl1035.11038MR1784410
- [CG] J.B. Conrey, A. Ghosh — A conjecture for the sixth power moment of the Riemann zeta-function, Internat. Math. Res. Notices15 (1998), 775-780. Zbl0920.11060MR1639551
- [CI1] B. Conrey, H. Iwaniec — The cubic moment of central values of automorphic L-functionsAnn. Math, 151, no. 3 (2000), 1175-1216 . Zbl0973.11056MR1779567
- [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. Zbl1007.11051MR1905090
- [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). MR1956231
- [CS] J.B. Conrey, K. Soundararajan — Real zeros of quadratic Dirichlet L-functions. Invent. Math.150, no. 1 (2002), 1-44. Zbl1042.11053MR1930880
- [De1] P. Deligne — La conjecture de Weil, I, Publ. Math. IHES43 (1974), 273- 308. Zbl0287.14001MR340258
- [De2] P. Deligne — La conjecture de Weil, II, Publ. Math. IHES52 (1981), 313- 428. Zbl0456.14014MR601520
- [Du] W. Duke — The critical order of vanishing of automorphic L-functions with high level, Invent. Math.119 (1995), 165-174. Zbl0838.11035MR1309975
- [DFI1] W. Duke, J. Friedlander, H. Iwaniec — Bounds for automorphic L-functions. Invent. Math.112, no. 1 (1993), 1-8. Zbl0765.11038MR1207474
- [DFI2] W. Duke, J. Friedlander, H. Iwaniec — Bounds for automorphic L-functions. II, Invent. Math.115 (1994). Zbl0812.11032MR1258904
- [DFI3] W. Duke, J. Friedlander, H. Iwaniec — Class group L-functions. Duke Math. J.79, no. 1 (1995), 1-56. Zbl0838.11058MR1340293
- [DFI4] W. Duke, J. Friedlander, H. Iwaniec — Bounds for automorphic L-functions. III, Invent. Math.143, 2 (2001), 221-248. Zbl1163.11325MR1835388
- [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. Zbl0051.30303MR58756
- [FI] E. Fouvry, H. Iwaniec — Low lying zeros of dihedral L functions. Preprint. Zbl1028.11055MR1953291
- [GoJ] R. Godement, H. Jacquet - Zeta functions of simple algebras. Lecture Notes in Math.260 (1972). Zbl0244.12011MR342495
- [GZ] W. Gross, D. Zagier — Heegner points and derivatives of L-series. Invent. Math.84, no. 2 (1986), 225-320. Zbl0608.14019MR833192
- [HB] D.R. Heath-Brown — The fourth power mean of Dirichlet's L-functions, Analysis1, no. 1 (1981), 25-32. Zbl0479.10027MR623640
- [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. Zbl1166.11326MR1756106
- [He] S. Helgason — Differential geometry, Lie groups, and symmetric spaces. Pure and Appl. Math.80, Academic Press (1978). Zbl0451.53038MR514561
- [ILS] H. Iwaniec, W. Luo, P. Sarnak — Low Lying Zeros of families of L-functions, Publ. IHES.91 (2001), 55-131. Zbl1012.11041MR1828743
- [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. Zbl0992.11037MR1815374
- [IS2] H. Iwaniec, P. Sarnak — Perspectives in the Analytic Theory of L functions. Preprint (2000). MR1826269
- [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. Zbl0473.12008MR618323
- [JPPS] H. Jacquet, I.I. Piatetskii-Shapiro, J.A. Shalika - Rankin-Selberg convolutions, Amer. J. Math.105, no. 2 (1983), 367-464. Zbl0525.22018MR701565
- [Ka] N.M. Katz — Gauss Sums, Kloosterman Sums and Monodromy Groups, Annals of Maths. Studies116, PUP. Zbl0675.14004
- [KSa] N.M. Katz, P. Sarnak — Random matrices, Frobenius eigenvalues, and monodromy. American Math. Soc. Colloquium Publications45 (1999). Zbl0958.11004MR1659828
- [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. Zbl1051.11047MR1794267
- [KSn2] J.P. Keating, N.C. Snaith — Random matrix theory and ζ(1/2 + it). Comm. Math. Phys.214, no. 1 (2000), 57-89. Zbl1051.11048
- [KM1] E. Kowalski, P. Michel — The analytic rank of J0(q) and zeros of automorphic L-functions, Duke Math. J.100, 503-547. Zbl1161.11359MR1719730
- [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. Zbl1020.11033MR1778299
- [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. Zbl1054.11026MR1784797
- [KMV3] E. Kowalski, P. Michel, J. Vanderkam — Rankin-Selberg L functions in the level aspect, Duke Math. J.114, no. 1 (2002), 123-191. Zbl1035.11018MR1915038
- [Me] M.L. Mehta — Random matrices. Second edition. Academic Press, Inc., Boston, MA, 1991. Zbl0780.60014MR1083764
- [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. Zbl0268.10023MR337821
- [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. Zbl0851.11036MR1353938
- [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. Zbl0777.11031MR1210146
- [P] A. Peng — Ph. D. Thesis, Princeton University2001.
- [Ro] E. Royer — Petits zéros de fonctions L de formes modulaires, Acta Arith.99, no. 2 (2001), 147-172.. Zbl0984.11024MR1847618
- [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. Zbl0866.11050MR1395406
- [Sa] P. Sarnak — Estimates for Rankin-Selberg L-functions and quantum unique ergodicity, J. Funct. Anal.184, no. 2 (2001), 419-453. Zbl1006.11022MR1851004
- [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. Zbl0061.08404MR22872
- [So] K. Soundararajan — Non-vanishing of quadratic Dirichlet L-functions at s = 1/2, Ann. of Math.152, No. 2, 447-488. Zbl0964.11034MR1804529
- [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. Zbl0042.07901MR882550
- [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. Zbl0431.10015MR646366
- [Zi] M. Zirnbauer — Riemannian symmetric superspaces and their origin in random-matrix theory. J. Math. Phys.37, no. 10 (1996), 4986-5018. Zbl0871.58005MR1411617
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