@article{ASENS_1981_4_14_1_77_0, author = {Harris, Michael}, title = {Special values of zeta functions attached to {Siegel} modular forms}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {77--120}, publisher = {Elsevier}, volume = {Ser. 4, 14}, number = {1}, year = {1981}, doi = {10.24033/asens.1398}, mrnumber = {82m:10046}, zbl = {0465.10022}, language = {en}, url = {http://archive.numdam.org/articles/10.24033/asens.1398/} }
TY - JOUR AU - Harris, Michael TI - Special values of zeta functions attached to Siegel modular forms JO - Annales scientifiques de l'École Normale Supérieure PY - 1981 SP - 77 EP - 120 VL - 14 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.24033/asens.1398/ DO - 10.24033/asens.1398 LA - en ID - ASENS_1981_4_14_1_77_0 ER -
%0 Journal Article %A Harris, Michael %T Special values of zeta functions attached to Siegel modular forms %J Annales scientifiques de l'École Normale Supérieure %D 1981 %P 77-120 %V 14 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.24033/asens.1398/ %R 10.24033/asens.1398 %G en %F ASENS_1981_4_14_1_77_0
Harris, Michael. Special values of zeta functions attached to Siegel modular forms. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 14 (1981) no. 1, pp. 77-120. doi : 10.24033/asens.1398. http://archive.numdam.org/articles/10.24033/asens.1398/
[1] Symmetric Squares of Zeta-Functions of Siegel's Modular Forms of Genus 2 (Trudy. Mat. Inst. Steklov, Vol. 142, 1976, pp. 22-45). | MR | Zbl
,[2] On Analytic Properties of the Standard Zeta-Functions of Siegel Modular Forms (Mat. Sbornik, Vol. 106, 1978, pp. 323-339). | MR | Zbl
and ,[3] On the Theory of θ-Functions, the Moduli of Abelian Varieties, and the Moduli of Curves (Ann. of Math., Vol. 75, 1962, pp. 342-381). | Zbl
,[4] Compactification of Arithmetic Quotients of Bounded Symmetric Domains (Ann. of Math., Vol. 84, 1966, pp. 442-528). | MR | Zbl
and ,[5] Introduction to Automorphic Forms, in Proc. Symp. Pure Math., Vol. IX, Amer. Math. Soc., Providence, 1966, pp. 199-210. | MR | Zbl
,[6] Travaux de Shimura (Sém. Bourbaki, Vol. 23, (1970/1971), No. 389). | Numdam | Zbl
,[7] Valeurs de fonctions L et périodes d'intégrales, in Proc. Symp. Pure Math., Vol. XXXIII, Amer. Math. Soc., Providence, 1979, Part 2, pp. 313-346. | MR | Zbl
,[8] Algèbres enveloppantes, Gauthier-Villars, Paris, 1974. | MR | Zbl
,[9] Holomorphe Differentialformen zu Kongruenzgruppen der Siegelschen Modulgruppe (Inv. Math., Vol. 30, 1975, pp. 181-196). | MR | Zbl
,[10] Analytic Continuation of Symmetric Squares (Mat. Sbornik, Vol. 107, 1978, pp. 323-346). | MR | Zbl
,[11] On the De Rham Cohomology of Algebraic Varieties (Publ. Math. I.H.E.S., Vol. 29, 1966). | Numdam | MR | Zbl
,[12] Representations of Semi-Simple Lie groups IV, V, VI (Am. J. Math., Vol. 77-78, 1955-1956). | MR | Zbl
,[13] Automorphic Forms on Semi-Simple Lie Groups (Lecture Notes in Math., 62, 1968). | MR | Zbl
,[14] A Note on Three Lemmas of Shimura (Duke Math., J., Vol. 46, 1979, pp. 871-879). | MR | Zbl
,[15] Intertwining Differential Operators for Mp (n, R) and SU(n, n) (Trans. A.M.S., Vol. 246, 1978, pp. 311-337). | MR | Zbl
,[16] Restrictions and Expansions of Holomorphic Representations (J. Fun. Anal., Vol. 34, 1979, pp. 29-53). | MR | Zbl
and ,[17] Algebraic Solutions of Differential Equations (p-Curvature and the Hodge Filtration) (Inv. Math., Vol. 18, 1972, pp. 1-118). | MR | Zbl
,[18] p-Adic Properties of Modular Schemes and Modular Forms, in Modular Functions of One Variable III (Lecture Notes in Math., No. 350, 1973, pp. 63-190). | MR | Zbl
,[19] p-Adic L-Functions for CM Fields (Inv. Math., Vol. 49, 1978, pp. 199-297). | MR | Zbl
,[20] On the Differentiation of De Rham Cohomology Classes with Respect to Parameters (J. Math. Kyoto Univ., Vol. 8, 1968, pp. 199-213). | MR | Zbl
and ,[21] Euler Products, New Haven, Yale University Press, 1971. | Zbl
,[22] Die Differentialgleichungen in der Theorie der Siegelschen Modulfunktionen (Math. Ann., Vol. 126, 1953, pp. 44-68). | MR | Zbl
,[23] Siegel's Modular Forms and Dirichlet Series (Lecture Notes in Math., No. 216, 1971). | MR | Zbl
,[24] Twists of Hecke Series and Their Values at Integer Points (Mat. Sbornik, Vol. 104, 1977, pp. 617-651). | Zbl
and ,[25] Geometric Invariant Theory, Springer-Verlag, Berlin, 1965. | MR | Zbl
,[26] Abelian Varieties, Oxford University Press, London, 1970. | MR | Zbl
,[27] Automorphic Forms of Singular Weight are Singular Forms (Math. Ann., Vol. 215, 1975, pp. 173-193). | MR | Zbl
,[28] Analytic Continuation of the Holomorphic Discrete Series, (Acta. Math., Vol. 136, 1976, pp. 1-59). | MR | Zbl
and ,[29] Theory of Spherical Functions on Reductive Algebraic Groups Over p-Adic Fields (Publ. Math. I.H.E.S., Vol. 18, 1963, pp. 1-69). | Numdam | MR | Zbl
,[30] Die Randwerte holomorpher Funktionen auf Hermitesch symmetrischen Raumen (Inv. Math., Vol. 9, 1969, pp. 61-80). | MR | Zbl
,[31] Séminaire H. Cartan 1957/1958, Fonctions Automorphes, Paris, Secrétariat Mathématique, 1958. | Zbl
[32] On Some Arithmetic Properties of Modular Forms of One and Several Variables (Ann. of Math., Vol. 102, 1975, pp. 491-515). | MR | Zbl
,[33] On the Fourier Coefficients of Modular Forms of Several Variables (Göttingen Nachr. Akad. Wiss., 1975, pp. 261-268). | MR | Zbl
,[34] The Special Values of the Zeta Functions Associated with Cusp Forms, (Comm. Pure Appl. Math., Vol. 29, 1976, pp. 783-804). | MR | Zbl
,[35] On the Periods of Modular Forms (Math. Ann., Vol. 229, 1977, pp. 211-221). | MR | Zbl
,[36] On the Derivatives of Theta Functions and Modular Forms (Duke Math. J., Vol. 44, 1977, pp. 365-387). | MR | Zbl
,[37] The Special Values of the Zeta Functions Associated with Hilbert modular forms, (Duke Math. J., Vol. 45, 1978, pp. 637-679). | MR | Zbl
,[38] On Certain Reciprocity-Laws for Theta Functions and Modular Forms (Acta. Math., Vol. 141, 1978, pp. 35-71). | MR | Zbl
,[39] On automorphic Forms on Unitary Groups of Order 3, preprint.
,[40] Einführung in die Theorie der Modulfunktionen n-ten Grades (Math. Ann., Vol. 116, 1939, pp. 617-657). | JFM | MR | Zbl
,[41] Symplectic Geometry (Am. J. Math., Vol. 65, 1943, pp. 1-86). | MR | Zbl
,[42] Harmonic Analysis on Homogeneous Spaces, Marcel Dekker, Inc., New York, 1973. | MR | Zbl
,[42a] Representations of Reductive Lie groups, in Proc. Symp. Pure Math., Vol. XXXIII, Amer. Math. Soc., Providence, 1979, Part 1, pp. 71-86). | MR | Zbl
,[43] Harmonic Analysis on Semi-Simple Lie Groups I, Springer-Verlag, Berlin, 1972. | Zbl
,[44] Introduction à l'étude des variétés kählériennes, nouvelle édition corrigée, Hermann, Paris, 1958. | Zbl
,[45] The Classical Groups, Princeton University Press, 1946.
,[46] Modular Forms Whose Fourier Coefficients Involve Zeta-Functions of Quadratic Fields, in Modular Functions of One Variable VI (Lecture Notes in Math., No. 627, 1977, pp. 105-170). | MR | Zbl
,[47] Special Values of Zeta Functions, and Eisenstein Series of Half Integral Weight (Am. J. Math., Vol. 102, 1980, pp. 219-240). | MR | Zbl
,[48] An Analytic Construction of Degenerating Abelian Varieties Over Complete Local Rings (Compositio Math., Vol. 24, 1972, pp. 239-272). | Numdam | MR | Zbl
,[49] On Factorization of Hecke Polynomials for the Symplectic Group of Genus n, (Math. U.S.S.R. Sbornik, Vol. 33, 1977, pp. 343-373). | Zbl
,[50] Euler Expansions of Theta-Transforms of Siegel Modular Forms of Degree n (Math. U.S.S.R. Sbornik, Vol. 34, 1978, pp. 259-300). | Zbl
,[51] Eisenstein Series and Fields of Definition (Compositio Math., Vol. 37, 1978, pp. 121-169). | Numdam | MR | Zbl
,[52] Singular Modular Forms and Singular Holomorphic Representations, in preparation.
and ,[53] "l-motifs" et formes automorphes, preprint.
,[54] The Multiplicative Arithmetic of Siegel Modular Forms (Russian Math. Surveys, Vol. 34, 1979, pp. 75-148). | MR | Zbl
,[55] The Rationality of Holomorphic Eisenstein Series [Inv. Math. (in press)]. | Zbl
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