Eisenstein series and fields of definition

Karel, M.

Compositio Mathematica, Tome 37 (1978) no. 2, pp. 121-169.

[1] A. Ash et al: Smooth Compactification of Locally Symmetric Varieties, Math. Sci. Press, Brookline, Massachusetts, 1976.

[2] W.L. Baily, Jr.: On the theory of θ-functions, the moduli of Abelian varieties, and the moduli of curves, Ann. of Math. 75 (1962) 342-381. | Zbl

[3] W.L. Baily, Jr.: On Hensel's lemma and exponential sums, Global Analysis: Papers in Honor of K. Kodaira (D.C. Spencer and S. Iyanga, ed.), Princeton University Press, Princeton, 1969, 85-100. | Zbl

[4] W.L. Baily, Jr.: Eisenstein series on tube domains, Problems in Analysis: A symposium in Honor of Salomon Bochner, R.C. Gunning, ed., Princeton University Press, Princeton, 1970, 139-156. | MR | Zbl

[5] W.L. Baily, Jr.: Automorphic forms with integral Fourier coefficients, Several Complex Variables I-Maryland 1970, Lecture Notes in Mathematics 155, Springer-Verlag, Berlin - Heidelberg - New York, 1970, 1-8. | Zbl

[6] W.L. Baily, Jr.: An exceptional arithmetic group and its Eisenstein series, Ann. of Math. 91 (1970) 512-549. | MR | Zbl

[7] W.L. Baily, Jr.: On the Fourier coefficients of certain Eisenstein series on the adèle group, Number Theory, Algebraic Geometry and Commutative Algebra: in honor of Y. Akizuki, Kinokuniya, Tokyo, 1973. | MR | Zbl

[8] W.L. Baily, Jr.: Introductory Lectures on Automorphic Forms, Publications of the Mathematical Society of Japan 12, Iwanami Shoten, Publishers, and Princeton University Press, Tokyo, 1973. | MR | Zbl

[9] W.L. Baily, Jr. and A. Borel: Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math. 84 (1966) 442-528. | MR | Zbl

[10] A. Borel: Some finiteness properties of adèle groups over number fields, Publ. Math. I.H.E.S. 16 (1963) 101-126. | Numdam | MR | Zbl

[11] A. Borel: Introduction to Automorphic Forms, in Algebraic Groups and Discontinuous Subgroups (A. Borel and G.D. Mostow, ed.): Proc. Symp. Pure Math. IX, Amer. Math. Soc., Providence, R. I., 1966, 199-210. | MR | Zbl

[12] A. Borel: Linear Algebraic Groups (Notes by H. Bass), Benjamin Lecture Notes Series, New York, 1969. | MR | Zbl

[13] A. Borel: personal communication.

[14] A. Borel and J. Tits: Groupes réductifs, Publ. Math. I.H.E.S. 27 (1965) 55-151. | Numdam | MR | Zbl

[15] A. Borel, Compléments à l'article "Groupes réductifs," Publ. Math. IHES. 41 (1972) 253-276. | Numdam | Zbl

[16] F. Bruhat and J. Tits: Groupes réductifs sur un corps local: I. Données radicielles valuées, Publ. Math. I.H.E.S. 41 (1972) 5-252. | Numdam | MR | Zbl

[17] C. Chevalley: Séminaire C. Chevalley 1956-1958: Classification des groupes de Lie algébriques, mimeographed notes, École Normal Supérieure, Paris, 1958. | Zbl

[18] U. Christian: Zur Theorie der Hilbert-Siegelschen Modulfunktionen, Math. Ann. 152 (1963) 275-341. | MR | Zbl

[19] U. Christian, Zur Theorie der Hilbert-Siegelschen Modulfunktionen über den Eisensteinreihen, Abhandl. math. Sem. Hamburg Univ. 27 (1964). | MR | Zbl

[20] P. Deligne: Travaux de Shimura, Séminaire Bourbaki, 1970/71, exposé 389, in Lecture Notes in Mathematics 244, Springer-Verlag, Berlin-Heidelberg -New York, 1971. | Numdam | MR | Zbl

[21] R. Godement: Introduction à la théorie de Langlands, Séminaire Bourbaki, 1966/67, exposé 321, W.A. Benjaminin, New York, and Amsterdam, 1968. | Numdam | Zbl

[22] R. Gunning: Lectures on Modular Forms, Princeton University Press, Princeton, 1962. | MR | Zbl

[23] E. Hecke: Analytische Arithmetik der positiven quadratischen Formen, Kgl. Danske Vid. Selsk. Math. - fys. Medd. XVII, 12 (1940), (Math. Werke; 789-918). | JFM | MR | Zbl

[24] S. Helgason: Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962. | MR | Zbl

[25] H. Klingen: Über den arithmetischen Charakter der Fourier koeffizienten von Modulformen, Math. Ann. 147 (1962) 176-188. | MR | Zbl

[26] H.D. Kloosterman: Theorie der Eisensteinschen Reihen von mehreren Veränderlichen, Abhandl. math. Sem. Hamburg Univ. 6 (1927) 163-188. | JFM

[27] M. Kneser: Starke Approximation in Algebraischen Gruppen. I, J. f. reine angew. Math. 218 (1965) 190-203. | MR | Zbl

[28] A. Koranyi and J. Wolf: Realization of Hermitian Symmetric Spaces as Generalized Half-Planes, Ann. of Math. 81 (1965) 265-288. | MR | Zbl

[29] A. Ogg: Modular Forms and Dirichlet Series, W.A. Benjamin, New York and Amsterdam, 1969. | MR | Zbl

[30] H. Petersson: Über den Körper der Fourierkoeffizienten der von Hecke untersuchten Eisensteinreihen, Abhandl. math. Sem. Hamburg Univ. 16 (1949) 101-113. | MR | Zbl

[31] G. Prasad: Strong approximation for semi-simple groups over function fields. Ann. of Math. 105 (1977) 553-572. | MR | Zbl

[32] G. Shimura: On canonical models of arithmetic quotients of bounded symmetric domains, I, II, Ann. of Math 91 (1970) 144-222; 92 (1970) 528-549. | MR | Zbl

[33] G. Shimura: On the Fourier coefficients of modular forms of several variables, Nachr. Akad. Wiss. Göttingen, 1975, Nr. 17. | MR | Zbl

[34] C.L. Siegel: Über die analytische Theorie der quadratischen Formen, Ann. of Math 36 (1935) 527-606 (Ges. Abhandl. I, 326-405). | JFM | MR | Zbl

[35] T.A. Springer: Jordan Algebras and Algebraic Groups, Springer-Verlag, NewYork-Heidelberg -Berlin, 1973. | Zbl

[36] L.-C. Tsao: The rationality of the Fourier coefficients of certain Eisenstein series on tube domains, Compositio Math. 32 (1976) 225-291. | Numdam | MR | Zbl

[37] L.-C. Tsao: On saturated subgroups, preprint.

[38] L.-C. Tsao: Saturated normal congruence subgroups of the modular group, preprint.

[39] E.B. Vinberg: Homogeneous cones, Soviet Math. 1 (1960) 787-793 (translated from Doklady Akad. Nauk SSSR 133 (1960)). | MR | Zbl

[40] A. Weil: Adèles and algebraic groups (Notes by M. Demazure and T. Ono), Institute for Advanced Study, Princeton, 1961. | MR

[41] A. Weil: Basic Number Theory. Springer-Verlag, Berlin-Heidelberg-New York, 1967. | MR | Zbl