Quelques applications du théorème de densité de Chebotarev
Serre, Jean-Pierre
Publications Mathématiques de l'IHÉS, Tome 54 (1981), p. 123-201 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{PMIHES_1981__54__123_0,
     author = {Serre, Jean-Pierre},
     title = {Quelques applications du th\'eor\`eme de densit\'e de Chebotarev},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     volume = {54},
     year = {1981},
     pages = {123-201},
     mrnumber = {83k:12011},
     zbl = {0496.12011},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/PMIHES_1981__54__123_0}
}

Serre, Jean-Pierre. Quelques applications du théorème de densité de Chebotarev. Publications Mathématiques de l'IHÉS, Tome 54 (1981) pp. 123-201. http://gdmltest.u-ga.fr/item/PMIHES_1981__54__123_0/

[1] E. Artin, Über eine neue Art von L-Reihen, Hamb. Abh., 3 (1923), 89-108 (= Coll. Papers, 105-124). | JFM 49.0123.01

[2] N. Bourbaki, Variétés différentielles et analytiques. Fascicule de résultats, Paris, Hermann, 1971. | Zbl 0217.20401

[3] N. Bourbaki, Groupes et Algèbres de Lie, chapitre II : « Algèbres de Lie libres » ; chapitre III : « Groupes de Lie », Paris, Hermann, 1972. | Zbl 0244.22007

[4] S. Chowla, On the least prime in an arithmetic progression, J. Indian Math. Soc., 1 (1934), 1-3. | JFM 60.0144.01 | Zbl 0009.00802

[5] R. Dedekind, Über die Diskriminanten endlicher Körper, Gött. Abh., 29 (1882), 1-56 (= Ges. Math. Werke, I, 351-397). | JFM 14.0059.02

[6] R. Dedekind, Vorlesungen über Zahlentheorie von P. G. Lejeune-Dirichlet, 4e éd., Braunschweig, 1893 (réimpr. : New York, Chelsea, 1968).

[7] P. Deligne, Formes modulaires et représentations ℓ-adiques, Sém. Bourbaki 1968-1969, exposé 355, Lecture Notes in Math., 179, Springer-Verlag, 1971, 139-172. | Numdam | Zbl 0206.49901

[8] P. Deligne, La conjecture de Weil, I, Publ. Math. I.H.E.S., 43 (1974), 273-307. | Numdam | MR 49 #5013 | Zbl 0287.14001

[9] P. Deligne et J.-P. Serre, Formes modulaires de poids 1, Ann. Sci. E.N.S., 4e série, 7 (1974), 507-530. | Numdam | MR 52 #284 | Zbl 0321.10026

[10] J. Dieudonné et A. Grothendieck, Critères différentiels de régularité pour les localisés des algèbres analytiques, J. of Algebra, 5 (1967), 305-324. | MR 34 #7560 | Zbl 0163.03201

[11] H. Federer, Geometric Measure Theory, Berlin, Springer-Verlag, 1969. | MR 41 #1976 | Zbl 0176.00801

[12] G. F. Frobenius, Über Beziehungen zwischen den Primidealen eines algebraischen Körpers und den Substitutionen seiner Gruppe, Sitz. Akad. Berlin (1896), 689-703 (= Ges. Abh., II, 719-733). | JFM 27.0091.04

[13] G. H. Hardy et J. E. Littlewood, Tauberian theorems concerning power series and Dirichlet series whose coefficients are positive, Proc. London Math. Soc., 2e série, 13 (1914), 174-191 (= G. H. HARDY, Coll. Papers, VI, 510-527). | JFM 45.0389.02

[14] G. H. Hardy et J. E. Littlewood, Some theorems concerning Dirichlet series, Messenger of Math., 43 (1914), 134-147 (= G. H. HARDY, Coll. Papers, VI, 542-555). | JFM 45.0390.01

[15] K. Hensel, Über die Entwicklung der algebraischen Zahlen in Potenzreihen, Math. Ann., 55 (1902), 301-336. | JFM 32.0208.01

[16] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann. of Math., 79 (1964), 109-326. | MR 33 #7333 | Zbl 0122.38603

[17] J. Igusa, Complex Powers and Asymptotic Expansions II, J. Crelle, 278-279 (1975), 307-321. | MR 53 #8018 | Zbl 0315.41029

[18] J. Igusa, Some observations on higher degree characters, Amer. J. of Math., 99 (1977), 393-417. | MR 56 #324 | Zbl 0373.12008

[19] N. Iwahori et H. Matsumoto, Several remarks on projective representations of finite groups, J. Fac. Sci. Univ. Tokyo, 10 (1964), 129-146. | MR 31 #4841 | Zbl 0125.01504

[20] H. D. Kloosterman, Asymptotische Formeln für die Fourierkoeffizienten ganzer Modulformen, Hamb. Abh., 5 (1927), 338-352. | JFM 53.0346.01

[21] M. I. Knopp et J. Lehner, Gaps in the Fourier series of automorphic forms (à paraître). | Zbl 0473.10022

[22] J. C. Lagarias, H. L. Montgomery et A. M. Odlyzko, A Bound for the Least Prime Ideal in the Chebotarev Density Theorem, Invent. Math., 54 (1979), 271-296. | MR 81b:12013 | Zbl 0401.12014

[23] J. C. Lagarias et A. M. Odlyzko, Effective Versions of the Chebotarev Density Theorem, Algebraic Number Fields (A. Fröhlich edit.), New York, Academic Press, 1977, 409-464. | MR 56 #5506 | Zbl 0362.12011

[24] S. Lang et H. Trotter, Frobenius Distributions in GL2-Extensions, Lect. Notes in Math., 504, Springer-Verlag, 1975. | MR 58 #27900 | Zbl 0329.12015

[25] R. P. Langlands, Automorphic representations, Shimura varieties and motives. Ein Märchen, Proc. Symp. Pure Math., 33, Amer. Math. Soc., 1979, t. 2, 205-246. | MR 83f:12010 | Zbl 0447.12009

[26] M. Lazard, Groupes analytiques p-adiques, Publ. Math. I.H.E.S., 26 (1965), 1-219. | Numdam | MR 35 #188 | Zbl 0139.02302

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

[28] B. Mazur, Modular curves and the Eisenstein ideal, Publ. Math. I.H.E.S., 47 (1978), 33-186. | Numdam | MR 80c:14015 | Zbl 0394.14008

[29] B. Mazur, Rational Isogenies of Prime Degree, Invent. Math., 44 (1978), 129-162. | MR 80h:14022 | Zbl 0386.14009

[30] J. Œsterlé, Versions effectives du théorème de Chebotarev sous l'hypothèse de Riemann généralisée, Astérisque, 61 (1979), 165-167. | Zbl 0418.12005

[31] A. Ogg, Abelian curves of 2-power conductor, Proc. Camb. Phil. Soc., 62 (1966), 143-148. | MR 34 #1320 | Zbl 0163.15403

[32] R. Rankin, Contribution to the theory of Ramanujan's function τ(n) and similar arithmetical functions, I, II, Proc. Camb. Phil. Soc., 35 (1939), 351-372. | JFM 65.0353.01 | MR 1,69d | Zbl 0021.39201

[33] K. Ribet, Galois Representations attached to Eigenforms with Nebentypus, Lect. Notes in Math., 601, Springer-Verlag, 1977, 17-52. | MR 56 #11907 | Zbl 0363.10015

[34] P. Robba, Lemmes de Schwarz et lemmes d'approximations p-adiques en plusieurs variables, Invent. Math., 48 (1978), 245-277. | MR 80e:32021 | Zbl 0392.12020

[35] I. Šafarevič, Corps de nombres algébriques (en russe), Proc. Int. Congr. Math., Stockholm (1962), 163-176 (trad. anglaise : Amer. Math. Transl. (2), vol. 31 (1963), 25-39).

[36] L. Schœnfeld, Sharper Bounds for the Chebyshev Functions θ(x) and ѱ(x), II, Math. of Comp., 30 (1976), 337-360. | MR 56 #15581b | Zbl 0326.10037

[37] S. Sen, Ramification in p-adic Lie Extensions, Invent. Math., 17 (1972), 44-50. | MR 47 #8490 | Zbl 0242.12012

[38] J.-P. Serre, Corps locaux, Paris, Hermann, 1980, 3e éd. (trad. anglaise, Local Fields, GTM 67, Springer-Verlag, 1979). | Zbl 0423.12017

[39] J.-P. Serre, Classification des variétés analytiques p-adiques compactes, Topology, 3 (1965), 409-412. | MR 31 #3421 | Zbl 0141.37403

[40] J.-P. Serre, Abelian ℓ-adic representations and elliptic curves, New York, Benjamin Publ., 1968. | MR 41 #8422 | Zbl 0186.25701

[41] J.-P. Serre, Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math., 15 (1972), 259-331. | MR 52 #8126 | Zbl 0235.14012

[42] J.-P. Serre, Divisibilité de certaines fonctions arithmétiques, L'Ens. Math., 22 (1976), 227-260. | MR 55 #7958 | Zbl 0355.10021

[43] J.-P. Serre, Modular forms of weight one and Galois representations, Algebraic Number Theory (A. Fröhlich edit.), New York, Academic Press, 1977, 193-268. | MR 56 #8497 | Zbl 0366.10022

[44] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Publ. Math. Soc. Japan, vol. II, Princeton Univ. Press, 1971. | Zbl 0221.10029

[45] H. Stark, Some effective cases of the Brauer-Siegel theorem, Invent. Math., 23 (1974), 135-152. | MR 49 #7218 | Zbl 0278.12005

[46] H. P. F. Swinnerton-Dyer, On ℓ-adic representations and congruences for coefficients of modular forms, Lecture Notes in Math., 350, Springer-Verlag, 1973, 1-55. | MR 53 #10717a | Zbl 0267.10032

[47] N. Tschebotareff, Die Bestimmung der Dichtigkeit einer Menge von Primzahlen, welche zu einer gegebenen Substitutionsklasse gehören, Math. Ann., 95 (1926), 191-228. | JFM 51.0149.04

[48] A. Weil, Zeta-functions and Mellin transforms, Proc. Bombay Coll. on Alg. Geometry, Bombay, Tata Institute, 1968, 409-426 (= Œuvres Sci., III, 179-196). | MR 41 #6857 | Zbl 0193.49104

[49] H. Weyl, On the volume of tubes, Amer. J. of Math., 61 (1939), 461-472 (= Ges. Abh., III, 658-669). | JFM 65.0796.01 | Zbl 0021.35503

[50] E. Wirsing, Das asymptotische Verhalten von Summen über multiplikative Funktionen, Math. Ann., 143 (1961), 75-102. | MR 24 #A1241 | Zbl 0104.04201