Automorphic forms and the periods of abelian varieties

Goro SHIMURA

doi:10.2969/jmsj/03130561

Goro SHIMURA

著者情報

ジャーナルフリー

1979 年 31 巻 3 号 p. 561-592

DOI https://doi.org/10.2969/jmsj/03130561

詳細

Published: 1979 Received: 1978/07/11 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) A. Borel and N. Wallach, Continuous cohomology, discrete subgroups and representations of reductive groups, to appear in Annals of Math, studies.
2) B. Gross, On the periods of abelian integrals and a formula of Chowla and Selberg, Invent. Math. 45 (1978), 193-211.
3) Kazhdan, Some applications of the Weil representation, preprint, 1976.
4) Y. Matsushima, On the first Betti number of compact quotient spaces of higher dimensional symmetric spaces, Ann. of Math., 75 (1962), 312-330.
5) K. Miyake, Models of certain automorphic function fields, Acta Math., 126 (1971), 245-307.
6) A. Selberg and S. Chowla, On Epstein's zeta-function, J. reine angew. Math., 227 (1967), 86-110.
7) G. Shimura, On analytic families of polarized abelian varieties and automorphic functions, Ann. of Math., 78 (1963), 149-192.
8) G. Shimura, On the field of definition for a field of automorphic functions, I, II, III, Ann. of Math., 80 (1964), 160-189; 81 (1965), 124-165; 83 (1966), 377-385.
9) G. Shimura, Construction of class fields and zeta functions of algebraic curves, Ann. of Math., 85 (1967), 58-159.
10) G. Shimura, Algebraic number fields and symplectic discontinuous groups, Ann. of Math., 86 (1967), 503-592.
11) 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.
12) G. Shimura, On some arithmetic properties of modular forms of one and several variables, Ann. of Math., 102 (1975), 491-515.
13) G. Shimura, On the derivatives of theta functions and modular forms, Duke Math. J., 44 (1977), 365-387.
14) G. Shimura, The arithmetic of automorphic forms with respect to a unitary group, Ann. of Math., 107 (1978), 569-605.
15) G. Shimura and Y. Taniyama, Complex multiplication of abelian varieties and its applications to number theory, Publ. Math. Soc. Japan, No. 6, 1961.
16) A. Weil, Sur les périodes aes intégrales abéliennes, Comm. Pure Appl. Math., 29 (1976), 813-819.
17) T. Kubota, On the field extension by complex multiplication, Trans. Amer. Math. Soc., 118 (1965), 113-122.

Right : [1] A. Borel and N. Wallach, Continuous cohomology, discrete subgroups and representations of reductive groups, to appear in Annals of Math. studies.
[2] B. Gross, On the periods of abelian integrals and a formula of Chowla and Selberg, Invent. Math. 45 (1978), 193-211.
[3] Kazhdan, Some applications of the Weil representation, preprint, 1976.
[4] Y. Matsushima, On the first Betti number of compact quotient spaces of higher dimensional symmetric spaces, Ann. of Math., 75 (1962), 312-330.
[5] K. Miyake, Models of certain automorphic function fields, Acta Math., 126 (1971), 245-307.
[6] A. Selberg and S. Chowla, On Epstein's zeta-function, J. reine angew. Math., 227 (1967), 86-110.
[7] G. Shimura, On analytic families of polarized abelian varieties and automorphic functions, Ann. of Math., 78 (1963), 149-192.
[8] G. Shimura, On the field of definition for a field of automorphic functions, I, II, III, Ann. of Math., 80 (1964), 160-189; 81 (1965), 124-165; 83 (1966), 377-385.
[9] G. Shimura, Construction of class fields and zeta functions of algebraic curves, Ann. of Math., 85 (1967), 58-159.
[10] G. Shimura, Algebraic number fields and symplectic discontinuous groups, Ann. of Math., 86 (1967), 503-592.
[11] 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.
[12] G. Shimura, On some arithmetic properties of modular forms of one and several variables, Ann. of Math., 102 (1975), 491-515.
[13] G. Shimura, On the derivatives of theta functions and modular forms, Duke Math. J., 44 (1977), 365-387.
[14] G. Shimura, The arithmetic of automorphic forms with respect to a unitary group, Ann. of Math., 107 (1978), 569-605.
[15] G. Shimura and Y. Taniyama, Complex multiplication of abelian varieties and its applications to number theory, Publ. Math. Soc. Japan, No. 6, 1961.
[16] A. Weil, Sur les périodes aes intégrales abéliennes, Comm. Pure Appl. Math., 29 (1976), 813-819.
[17] T. Kubota, On the field extension by complex multiplication, Trans. Amer. Math. Soc., 118 (1965), 113-122.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

責任著者(Corresponding author)

訂正情報

J-STAGEへの登録はこちら（無料）