Répartition asymptotique des valeurs propres de l’opérateur de Hecke 𝑇_𝑝

Serre, Jean-Pierre¹

¹ Collège de France, 3 rue d’Ulm, F-75231 Paris Cedex 05, France

Journal of the American Mathematical Society, Tome 10 (1997) no. 1, pp. 75-102

Détail

DOI : 10.1090/S0894-0347-97-00220-8

Bibliographie

[1] Atkin, A. O. L., Lehner, J. Hecke operators on Γ₀(𝑚) Math. Ann. 1970 134 160

[2] Bourbaki, N. Éléments de mathématique. Fasc. XIII. Livre VI: Intégration. Chapitres 1, 2, 3 et 4: Inégalités de convexité, Espaces de Riesz, Mesures sur les espaces localement compacts, Prolongement d’une mesure, Espaces 𝐿^{𝑝} 1965 283

[3] Brumer, Armand The rank of 𝐽₀(𝑁) Astérisque 1995

[4] Cartier, P. Harmonic analysis on trees 1973 419 424

[5] Cohen, Henri Trace des opérateurs de Hecke sur Γ₀(𝑁) 1977

[6] Cox, David A., Parry, Walter R. Genera of congruence subgroups in 𝑄-quaternion algebras J. Reine Angew. Math. 1984 66 112

[7] Ekedahl, Torsten, Serre, Jean-Pierre Exemples de courbes algébriques à jacobienne complètement décomposable C. R. Acad. Sci. Paris Sér. I Math. 1993 509 513

[8] Evertse, J.-H., Silverman, J. H. Uniform bounds for the number of solutions to 𝑌ⁿ Math. Proc. Cambridge Philos. Soc. 1986 237 248

[9] Nakayama, Tadasi On Frobeniusean algebras. I Ann. of Math. (2) 1939 611 633

[10] Hashimoto, Ki-Ichiro Zeta functions of finite graphs and representations of 𝑝-adic groups 1989 211 280

[11] Huxley, M. N. A note on polynomial congruences 1981 193 196

[12] Igusa, Jun-Ichi Kroneckerian model of fields of elliptic modular functions Amer. J. Math. 1959 561 577

[13] Ihara, Yasutaka On discrete subgroups of the two by two projective linear group over 𝔭-adic fields J. Math. Soc. Japan 1966 219 235

[14] Ihara, Yasutaka Some remarks on the number of rational points of algebraic curves over finite fields J. Fac. Sci. Univ. Tokyo Sect. IA Math. 1981

[15] Lubotzky, Alexander Discrete groups, expanding graphs and invariant measures 1994

[16] Lubotzky, A., Phillips, R., Sarnak, P. Ramanujan graphs Combinatorica 1988 261 277

[17] Mautner, F. I. Spherical functions over 𝔓-adic fields. I Amer. J. Math. 1958 441 457

[18] Mckay, Brendan D. The expected eigenvalue distribution of a large regular graph Linear Algebra Appl. 1981 203 216

[19] Mestre, J.-F. La méthode des graphes. Exemples et applications 1986 217 242

[20] Ribet, Kenneth A. Twists of modular forms and endomorphisms of abelian varieties Math. Ann. 1980 43 62

[21] Rohlfs, Jã¼Rgen, Speh, Birgit On limit multiplicities of representations with cohomology in the cuspidal spectrum Duke Math. J. 1987 199 211

[22] Savin, Gordan Limit multiplicities of cusp forms Invent. Math. 1989 149 159

[23] Schoof, Renã©, Van Der Vlugt, Marcel Hecke operators and the weight distributions of certain codes J. Combin. Theory Ser. A 1991 163 186

[24] Serre, Jean-Pierre Arbres, amalgames, 𝑆𝐿₂ 1977

[25] Serre, Jean-Pierre Sur le nombre des points rationnels d’une courbe algébrique sur un corps fini C. R. Acad. Sci. Paris Sér. I Math. 1983 397 402

[26] Shahidi, Freydoon Symmetric power 𝐿-functions for 𝐺𝐿(2) 1994 159 182

[27] Shimura, Goro Introduction to the arithmetic theory of automorphic functions 1971

[28] Shimura, Goro On the factors of the jacobian variety of a modular function field J. Math. Soc. Japan 1973 523 544

[29] Silberger, Allan J. 𝑃𝐺𝐿₂ over the 𝑝-adics: its representations, spherical functions, and Fourier analysis 1970

[30] Tsfasman, Michael A. Some remarks on the asymptotic number of points 1992 178 192