Multiplicity one theorem and modular symbols

Kazuyuki HATADA

doi:10.2969/jmsj/03330445

Kazuyuki HATADA

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JOURNAL FREE ACCESS

1981 Volume 33 Issue 3 Pages 445-470

DOI https://doi.org/10.2969/jmsj/03330445

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Published: 1981 Received: May 04, 1977 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: AFFILIATION Details: Wrong :
1) Department of Mathematics Faculty of Science University of Tokyo
2) Department of Mathematics Faculty of Education Gifu Universiy

Right :
1) Department of Mathematics Faculty of Science University of Tokyo
2) Department of Mathematics Faculty of Education Gifu University

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) A. Atkin and J. Lehner, Hecke operators on Γ₀(m), Math. Ann., 185 (1970), 134-160.
2) B. Birch, Elliptic curves, a progress report, In: A.M.S. conference on number theory, Stonybrook, 396-400, American Mathematical Society, Providence, 1969.
3) P. Deligne, La conjecture de Weil I, Publ. Math. I.H.E.S., 43 (1974), 273-307.
4) K. Doi and T. Miyake, Automorphic forms and number theory, Kinokuniya, Tokyo, 1976 (in Japanese).
5) M. Eichler, Eine Verallgemeinerung der Abelschen Integrale, Math. Z., 67 (1957), 267-298.
6) K. Hatada, On the divisibility by 2 of the Eigenvalues of Hecke operators, Proc. Japan Acad., 53A (1977), 37-40.
7) K. Hatada, Congruences of the Eigenvalues of Hecke operators, Proc. Japan Acad., 53A (1977), 125-128.
8) K. Hatada, Periods of primitive forms, Proc. Japan Acad., 53A (1977), 174-177.
9) K. Hatada, On the rationality of periods of primitive forms, to appear in Acta Arithmetica Vol. 40, No. 1.
10)K. Hatada, Congruences for the coefficients of cusp forms on Γ₀(N), (Eigenvalues of Hecke operators on some congruence subgroups), 1978 (preprint).
11) Y. Manin, Parabolic points and zeta functions of modular curves, Izv. Acad. Nauk, 6 (1972), AMS translation, 19-64.
12) Y. Manin, Periods of parabolic forms and p-adic Hecke series, Math. Sbornik, 21 (1973), AMS translation, 371-393.
13) B. Mazur, Courbes elliptiques et symboles modulaires, Séminaire Bourbaki, 24e année, n°414 (1971/72).
14) G. Shimura, Sur les intégrales attachées aux formes automorphes, J. Math. Soc. Japan, 11 (1959), 291-311.
15) G. Shimura, Introduction to the arithmetic theory of automorphic functions, Iwanami and Princeton university press, Tokyo and Princeton, 1971.
16) G. Shimura, The special values of the zeta functions associated with cusp forms, Comm. Pure Appl. Math., 29 (1976), 783-804.
17) G. Shimura, On the periods of modular forms, Math. Ann., 229 (1977), 211-221.
18) S. Lang, Rapport sur la cohomologie des groupes, Benjamin, New York, 1966.
19) S. Lang, Introduction to modular forms, Springer, Berlin-Heidelberg-New York, 1976.

Right : [1] A. Atkin and J. Lehner, Hecke operators on Γ₀(m), Math. Ann., 185 (1970), 134-160.
[2] B. Birch, Elliptic curves, a progress report, In: A. M. S. conference on number theory, Stonybrook, 396-400, American Mathematical Society, Providence, 1969.
[3] P. Deligne, La conjecture de Weil I, Publ. Math. I. H. E. S., 43 (1974), 273-307.
[4] K. Doi and T. Miyake, Automorphic forms and number theory, Kinokuniya, Tokyo, 1976 (in Japanese).
[5] M. Eichler, Eine Verallgemeinerung der Abelschen Integrale, Math. Z., 67 (1957), 267-298.
[6] K. Hatada, On the divisibility by 2 of the Eigenvalues of Hecke operators, Proc. Japan Acad., 53A (1977), 37-40.
[7] K. Hatada, Congruences of the Eigenvalues of Hecke operators, Proc. Japan Acad., 53A (1977), 125-128.
[8] K. Hatada, Periods of primitive forms, Proc. Japan Acad., 53A (1977), 174-177.
[9] K. Hatada, On the rationality of periods of primitive forms, to appear in Acta Arithmetica Vol. 40, No. 1.
[10] K. Hatada, Congruences for the coefficients of cusp forms on Γ₀(N), (Eigenvalues of Hecke operators on some congruence subgroups), 1978 (preprint).
[11] Y. Manin, Parabolic points and zeta functions of modular curves, Izv. Acad. Nauk, 6 (1972), AMS translation, 19-64.
[12] Y. Manin, Periods of parabolic forms and p-adic Hecke series, Math. Sbornik, 21 (1973), AMS translation, 371-393.
[13] B. Mazur, Courbes elliptiques et symboles modulaires, Séminaire Bourbaki, 24e année, n°414 (1971/72).
[14] G. Shimura, Sur les intégrales attachées aux formes automorphes, J. Math. Soc. Japan, 11 (1959), 291-311.
[15] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Iwanami and Princeton university press, Tokyo and Princeton, 1971.
[16] G. Shimura, The special values of the zeta functions associated with cusp forms, Comm. Pure Appl. Math., 29 (1976), 783-804.
[17] G. Shimura, On the periods of modular forms, Math. Ann., 229 (1977), 211-221.
[18] S. Lang, Rapport sur la cohomologie des groupes, Benjamin, New York, 1966.
[19] S. Lang, Introduction to modular forms, Springer, Berlin-Heidelberg-New York, 1976.

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

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