Automorphic forms and the periods of abelian varieties

Goro SHIMURA

doi:10.2969/jmsj/03130561

Goro SHIMURA

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JOURNAL FREE ACCESS

1979 Volume 31 Issue 3 Pages 561-592

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

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Published: 1979 Received: July 11, 1978 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: 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.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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