References
A. Ash, D. Mumford, M. Rapoport andY. Tai, Smooth Compactification of Locally Symmetric Varieties, Math. Sci. Press, Brookline, Massachusetts 1976.
W.L. Baily, Jr., On Hensel’s Lemma and Exponential Sums, in Global Analysis: Papers in Honor of K. Kodaira (D.C. Spencer and S. Iyanaga, ed.), 85–100, Princeton University Press, Princeton 1969.
W.L. Baily, Jr., An Exceptional Arithmetic Group and its Eisenstein Series, Ann. of Math.91 (1970), 512–549.
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.
W.L. Baily, Jr., Introductory Lectures on Automorphic Forms, Publications of the Mathematical Society of Japan12, Iwanami Shoten, Publishers, and Princeton University Press, Tokyo 1973.
W.L. Baily, Jr., Arithmetic Hilbert Modular Functions II, Revista Mat. Iberoamericana1 (1985), 85–119.
W.L. Baily, Jr., On the Proof of the Reciprocity Law for Arithmetic Siegel Modular Functions, Proc. Indian Acad. Sci. Math. Sci.97 (1987), no. 1-3 (1988), 21–30.
W. L. Baily, Jr.,A. Borel, Compactification of Arithmetic Quotients of Bounded Symmetric Domains, Ann. of Math.84 (1966), 442–528.
A. Borel, Some Finiteness Properties of Adele Groups over Number Fields, Publ. Math. Inst. Hautes Etud. Sci.16 (1963), 5–30.
A. Borel, Linear Algebraic Groups (Notes by H. Bass), Benjamin Lecture Notes Series, Benjamin, New York 1969.
A. Borel, J.-P. Serre, Corners and Arithmetic Groups, Comment. Math. Helv.48 (1973), 436–491.
A. Borel, J. Tits, Groupes réductifs, Publ. Math. I.H.E.S.27 (1965), 55–151.
A. Borel, J. Tits, Compléments à l’article ‘Groupes réductifs’, Publ. Math. I.H.E.S.41 (1972), 253–276.
F. Borel, J. Tits, Homomorphismes ‘abstraits’ de groupes algébriques simples, Ann. Math. (2)97 (1972), 499–521.
M.V. Borovoi, Conjugation of Shimura Varieties, Proc. Internat. Congr. Math. (Berkeley, 1986), Vol.1, Amer. Math. Soc, Providence 1987.
H. Braun, Hermitian Modular Functions, -- II,-- III, Ann. of Math.50 (1949), 827–855;,51 (1950), 92-104;53 (1951), 143-160.
H. Braun, M. Koecher, Jordan-Algebren, Springer-Verlag, Berlin-Heidelberg-New York 1966.
C. Chevalley, Deux theorèmes d’arithmétique, J. Math. Soc. Japan3 (1951), 36–44.
P. Deligne Travaux de Shimura, Sém. Bourbaki Février 1971, Exposé 389, Lecture Notes in Math.244, Springer-Verlag, Berlin-Heidelberg-New York 1971.
P. Feit, Poles and Residues of Eisenstein Series for Symplectic and Unitary Groups, Memoirs of the Amer. Math. Society61, AMS, Providence 1986.
M. Harris, Arithmetic Vector Bundles and Automorphic Forms on Shimura Varieties I, Invent. Math82 (1985), 151–189.
M. Harris, Arithmetic Vector Bundles and Automorphic Forms on Shimura Varieties II, Comp. Math.60 (1986), 323–378.
E. Hecke, Analytische Funktionen und Algebraische Zahlen II, Abh. Math. Sem. Univ. Hamburg3 (1924), 213–236.
E. Hecke, Theorie der Eisensteinschen Reihen höherer Stufe und ihre Anwendung auf Funktionentheorie und Arithmetik, Abh. Math. Sem. Univ. Hamburg5 (1927), 199–224.
E. Hecke, Analytische Arithmetik der positiven quadratischen Formen, Kg. Danske Vid. Selsk. Math.-fys. Medd. XIII,12 (1940).
C.S. Herz, Bessel Functions of Matrix Argument, Ann. of Math.61 (1955), 474–523.
M.L. Karel, Eisenstein Series and Fields of Definition, Comp. Math.37 (1978), 121–169.
H. Klingen, Über die Werte der Dedekindschen Zetafunktion, Math. Ann.145 (1962), 265–272.
H. Klingen, Über den arithmetischen Charakter der Fourierkoeffizienten von Modulformen, Math. Ann.147 (1962), 176–188.
H.D. Kloosterman, Theorie der Eisensteinschen Reihen von mehreren Veränderlichen, Abh. Math. Sem. Univ. Hamburg6 (1928), 163–188.
M. Kneser, Starke Approximation in Algebraischen Gruppen I, J. reine angew. Math.218 (1965), 190–203.
A. Koranyi, J. Wolf, Realization of Hermitian Symmetric Spaces as Generalized Half-planes, Ann. of Math.81 (1965), 265–288.
J.S. Milne, Canonical Models of (Mixed) Shimura Varieties and Automorphic Vector Bundles, Automorphic Forms, Shimura Varieties andL-functions, Academic Press (1990).
T. Ono, Arithmetic of Algebraic Tori, Ann. of Math.74 (1961), 101–139.
H. Petersson, Über den Körper der Fourierkoeffizienten der von Hecke untersuchten Eisensteinreihen, Abh. Math. Sem. Univ. Hamburg16 (1949), 101–112.
G. Prasad Strong Approximation for Semi-simple Groups over Function Fields, Ann. of Math.5(1977), 553–572.
I. Satake Algebraic Structures of Symmetric Domains, Publications of the Math. Soc. of Japan14, Iwanami Shoten, Publishers, and Princeton University Press, Princeton 1980.
I. Satake, S. Ogata, Zeta Functions Associated to Cones and Their Special Values, in: Advanced Studies in Pure Math.15, Automorphic Forms and Geometry of Arithmetic Varieties, 1–27, Academic Press, Boston 1989.
G. Shimura, Construction of Class Fields and Zeta Functions of Algebraic Curves, Ann. of Math.85 (1967), 58–159.
G. Shimura, On Canonical Models of Arithmetic Quotients of Bounded Symmetric Domains I, II, Ann. of Math.91 (1970);92 (1970), 528–549.
G. Shimura, On Some Arithmetic Properties of Modular Forms of One and Several Variables, Ann. of Math.102 (1975), 491–515.
G. Shimura, Confluent Hypergeometric Functions on Tube Domains, Math. Ann.260 (1982), 269–302.
G. Shimura On Eisenstein Series, Duke Math. J.50 (1983), 417–476.
T. Shintani, On Evaluation of Zeta Functions of Totally Real Algebraic Number Fields at Non-positive Integers, J. Fac. Sci. Univ. Tokyo, Sec. IA,23 (1976), 393–417.
C.L. Siegel, Einführung in der Theorie Modulfunktionenn – ten Grades, Math. Ann.116 (1939), 617–657.
C.L. Siegel, Uber die Fourierschen Koeffizienten von Eisensteinschen Reihen der StufeT, Math. Zeitschr.105 (1968), 257–266.
C.L. Siegel, Berechnung von Zetafunktionen an ganzzahligen Stellen, Göttingen Nachr. Akad. Wiss. 196910, 87–102.
C.L. Siegel, Über die Fourierschen Koeffizienten von Modulformen, Göttingen Nachr. Akad. Wiss. 19703, 15–56.
T.A. Springer, Jordan Algebras and Algebraic Groups, Springer-Verlag, New York-Heidelberg-Berlin 1973.
J. Sturm, The Critical Values of Zeta Functions Associated to the Symplectic Group, Duke Math. J.48 (1981), 327–350.
L.-C. Tsao, The Rationality of the Fourier Coefficients of Certain Eisenstein Series on Tube Domains, Comp. Math.32 (1976), 225–291.
E.B. Vinberg, Homogeneous Cones, Soviet Math.1 (1960), 787–793; translated from Doklady Akad. Nauk SSSR133 (1960).
W.C. Waterhouse, Introduction to Affine Group Schemes, Springer-Verlag, New York-Heidelberg-Berlin 1979.
A. Weil, Adeles and Algebraic Groups (Notes by M. Demazure and T. Ono), Institute for Advanced Study, Princeton 1961.
A. Weil, Basic Number Theory, Springer-Verlag, Berlin-Heidelberg-New York 1967.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Karel, M.L. Eisenstein series on tube domains. Abh.Math.Semin.Univ.Hambg. 62, 81–116 (1992). https://doi.org/10.1007/BF02941620
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02941620