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On Artin L-functions associated to Hilbert modular forms of weight one. (English) Zbl 0523.12009


MSC:

11R39 Langlands-Weil conjectures, nonabelian class field theory
11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
11F70 Representation-theoretic methods; automorphic representations over local and global fields
11R80 Totally real fields
11R52 Quaternion and other division algebras: arithmetic, zeta functions
22E46 Semisimple Lie groups and their representations

Citations:

Zbl 0321.10026
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References:

[1] Artin, E., Tate, J.: Class field theory. New York: Benjamin 1967 · Zbl 1179.11040
[2] Baily, W., Borel, A.: Compactification of arithmetic quotients of bounded symmetric domains. Ann. of Math.84, 442-528 (1966) · Zbl 0154.08602
[3] Borel, A., Casselman, W.: Automorphic forms, representations andL-functions. Proc. Sympos. Pure Math., Vol. XXXIII, AMS, Providence, 1979 · Zbl 0403.00003
[4] Borel, A., Wallach, N.: Continuous cohomology, discrete subgroups, and representations of reductive groups. Ann. of Math. Studies94, Princeton U. Press, 1980 · Zbl 0443.22010
[5] Brumer, A.: On the units of algebraic number fields. Mathematika14, 121-124 (1967) · Zbl 0171.01105
[6] Brylinski, J.L., Labesse, J.P.: Cohomologie d’intersection et fonctionsL de certaines varietes de Shimura, Preprint · Zbl 0553.12005
[7] Buhler, J.P.: Icosahedral galois representations. Lecture Notes in Math., vol. 654. Berlin-Heidelberg-New York: Springer 1978 · Zbl 0374.12002
[8] Casselman, W.: The restriction of a representation ofGL 2(k) to GL2(O). Math. Ann.206, 311-318 (1973) · Zbl 0253.20062
[9] Casselman, W.: An assortment of results on representations ofGL 2(k). Proc. 1972 Antwerp Summer School. Lecture Notes in Math., vol. 349, pp. 1-54. Berlin-Heidelberg-New York: Springer 1973
[10] Curtis, C., Reiner, I.: Representation theory of finite groups and associative algebras. New York: Interscience 1962 · Zbl 0131.25601
[11] Deligne, P.: Travaux de Shimura, Sém. Bourbaki Février 71, Exposé 389, Lecture Notes in Math., vol. 244. Berlin-Heidelberg-New York: Springer 1971
[12] Deligne, P.: La Conjecture de Weil, II. Publ. Math. IHES52, 137-252 (1980)
[13] Deligne, P., Ribet, K.: Values of AbelianL-functions at negative integers over totally real fields. Invent. Math.59, 227-286 (1980) · Zbl 0434.12009
[14] Deligne, P., Serre, J-P.: Formes modulaires de poids 1. Ann. Sci. Ecole Norm. Sup. (4)7, 507-530 (1974) · Zbl 0321.10026
[15] Feit, W.: The current situation in the theory of finite simple groups. Actes Congres Intern. Math. 1970, t.1, 55-93
[16] Gelbart, S., Jacquet, H.: A relation between automorphic forms onGL 2 andGL 3. Ann. Sci. Ecole Norm. Sup. (4)11, 471-542 (1978) · Zbl 0406.10022
[17] Harder, G., Langlands, R.P., Rapoport, M.: Algebraische Zykeln auf Hilbert-Blumenthal-Flächen. Preprint · Zbl 0575.14004
[18] hartshorne, R.: Algebraic geometry. Berlin-Heidelberg-New York: springer 1977 · Zbl 0367.14001
[19] Jacquet, H., Piatetski-Shapiro, I.I., Shalika, J.A.: Automorphic Forms onGL(3). Ann. of Math.109, 169-212 (1979) · Zbl 0401.10037
[20] Jacquet, H., Langlands, R.P.: Automorphic Forms onGL(2). Lecture Notes in Math., vol. 114. Berlin-Heidelberg-New York: Springer 1970 · Zbl 0236.12010
[21] Jacquet, H., Shalika, J.A.: On Euler products and the classification of automorphic forms I and II. Amer. J. Math.103, (No. 3) 499-558; (No. 4) 777-815 (1981) · Zbl 0473.12008
[22] Katz, N.:p-adic Properties of Modular Schemes and Modular Forms, Proc. 1972, Antwerp Summer School, Lecture Notes in Math., vol. 350, pp. 70-189 Berlin-Heidelberg-New York: Springer 1973 · Zbl 0271.10033
[23] Katz, N.:p-adicL-functions forCM fields. Invent. Math.49, 199-297 (1978) · Zbl 0417.12003
[24] Knutson, D.: Algebraic spaces. Lecture Notes in Math., vol. 203. Berlin-Heidelberg-New York: Springer 1971 · Zbl 0221.14001
[25] Labesse, J.P., Langlands, R.P.:L-indistinguishability forSL(2). Can. J. Math., vol. XXXI (no. 4) 726-785 (1979) · Zbl 0421.12014
[26] Langlands, R.P.: Modular forms andl-adic representations, Proc. 1972 Antwerp summer School, Lecture Notes in Math. vol. 349, pp. 361-500. Berlin-Heidelberg-New York: Springer 1973
[27] Langlands, R.P.: On the zeta-functions of some simple Shimura varieties. Can. J. Math. vol. XXXI, (no. 6) 1121-1216 (1979) · Zbl 0444.14016
[28] Langlands, R.P.: Base Change forGL(2). Ann. of Math. Studies 96, Princeton U. Press, 1980 · Zbl 0444.22007
[29] Milne, J.S.: Etale Cohomology. Princeton U. Press 1980
[30] Rapoport, M.: Compactifications de l’espace de modules de Hilbert-Blumenthal. Compositio Math.36, (fasc. 3) 255-335 (1978) · Zbl 0386.14006
[31] Serre, J-P.: Modular forms of weight one and Galois representations. In: Algebraic Number Fields, pp. 193-268. London: Academic Press 1977
[32] Tunnell, J.B.: Artin’s Conjecture for Octahedral Representations. Bull. AMS (New Series)5, 173-175 (1981) · Zbl 0475.12016
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