Hecke polynomials of modular groups and congruence zeta functions of fibre varieties

Yasuo MORITA

doi:10.2969/jmsj/02140617

Yasuo MORITA

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ジャーナルフリー

1969 年 21 巻 4 号 p. 617-637

DOI https://doi.org/10.2969/jmsj/02140617

詳細

Published: 1969 Received: 1969/01/30 Available on J-STAGE: 2006/09/29 Accepted: - Advance online publication: - Revised: -
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訂正日: 2006/09/29 訂正理由: - 訂正箇所: 論文受付日訂正内容: 訂正前 : 19690630
訂正後 : 19690130

訂正日: 2006/09/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) M. Deuring, Die Typen der Multiplicatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Univ. Hamburg, 14 (1941), 197-272.
2) M. Deuring, Invarianten und Normalformen elliptischer Funktionenkörper, Math. Z., 47 (1941), 47-56.
3) M. Deuring, Die Struktur der elliptischen Funktionenkörper und die Klassenkörper der imaginären quadratische Zahlkörper, Math. Ann., 124 (1952), 393-426.
4) M. Eichler, Eine Verallgemeinerung der Abelschen Integral, Math. Z., 67 (1957), 267-298.
5) Y. Ihara, Hecke polynomials as congruence ζ functions in elliptic modular case, Ann. of Math., 85 (1967), 267-295 (cited HP)).
6) Y. Ihara, On Congruence Monodromy Problems, Vol. 1, Lecture note at University of Tokyo, 1968 (cited CMP) Vol. 1).
7) Y. Ihara, On Congruence Monodromy Problems, Vol. 2, Lecture note at University of Tokyo, 1969 (cited CMP) Vol. 2).
8) M. Kuga and G. Shimura, On the zeta function of fibre variety whose fibres, are abelian varieties, Ann. of Math., 82 (1965), 478-539.
9) M. Mennicke, On Ihara's modular group, Invent. Math., 4 (1967), 202-228.
10) A. Selberg, Harmonic analysis and discontinuous groups on weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc., 20 (1956), 47-87.
11) G. Shimura, Construction of class fields and zeta functions of algebraic curves, Ann. of Math., 85 (1967), 58-159.
12) G. Shimura and Y. Taniyama, Complex multiplication of abelian varieties and its applications to number theory, Publ. Math. Soc. Japan, 1961.
13) J. Tate, Endomorphisms of Abelian Varieties over Finite Fields, Invent. Math., 2 (1966), 134-144.

Right : [1] M. Deuring, Die Typen der Multiplicatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Univ. Hamburg, 14 (1941), 197-272.
[2] M. Deuring, Invarianten und Normalformen elliptischer Funktionenkörper, Math. Z., 47 (1941), 47-56.
[3] M. Deuring, Die Struktur der elliptischen Funktionenkörper und die Klassenkörper der imaginären quadratische Zahlkörper, Math. Ann., 124 (1952), 393-426.
[4] M. Eichler, Eine Verallgemeinerung der Abelschen Integral, Math. Z., 67 (1957), 267-298.
[5] Y. Ihara, Hecke polynomials as congruence ζ functions in elliptic modular case, Ann. of Math., 85 (1967), 267-295 (cited [HP]).
[6] Y. Ihara, On Congruence Monodromy Problems, Vol. 1, Lecture note at University of Tokyo, 1968 (cited [CMP]) Vol. 1).
[7] Y. Ihara, On Congruence Monodromy Problems, Vol. 2, Lecture note at University of Tokyo, 1969 (cited [CMP]) Vol. 2).
[8] M. Kuga and G. Shimura, On the zeta function of fibre variety whose fibres, are abelian varieties, Ann. of Math., 82 (1965), 478-539.
[9] M. Mennicke, On Ihara's modular group, Invent. Math., 4 (1967), 202-228.
[10] A. Selberg, Harmonic analysis and discontinuous groups on weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc., 20 (1956), 47-87.
[11] G. Shimura, Construction of class fields and zeta functions of algebraic curves, Ann. of Math., 85 (1967), 58-159.
[12] G. Shimura and Y. Taniyama, Complex multiplication of abelian varieties and its applications to number theory, Publ. Math. Soc. Japan, 1961.
[13] J. Tate, Endomorphisms of Abelian Varieties over Finite Fields, Invent. Math., 2 (1966), 134-144.

訂正日: 2006/09/29 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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