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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JOURNAL FREE ACCESS

1969 Volume 21 Issue 4 Pages 617-637

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

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Published: 1969 Received: January 30, 1969 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: DTRECEIVED Details: Wrong : 19690630
Right : 19690130

Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: 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.

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