On indefinite modular forms of weight one

Toyokazu HIRAMATSU; Noburo ISHII; Yoshio MIMURA

doi:10.2969/jmsj/03810067

Toyokazu HIRAMATSU, Noburo ISHII, Yoshio MIMURA

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1986 Volume 38 Issue 1 Pages 67-83

DOI https://doi.org/10.2969/jmsj/03810067

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Published: 1986 Received: September 05, 1984 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) E. Hecke, Über einen neuen Zusammenhang zwischen elliptischen Modulfunktionen und indefiniten quadratischen Formen, Mathematische Werke, Vandenhoeck & Ruprecht, Göttingen, 1959, 418-427.
2) E. Hecke, Zur Theorie der elliptischen Modulfunktionen, Mathematische Werke, Vandenhoeck & Ruprecht, Göttingen, 428-460.
3) T. Hiramatsu, Higher reciprocity laws and modular forms of weight one, Comm. Math. Univ. St. Paul., 31 (1982), 75-85.
4) T. Hiramatsu and Y. Mimura, The modular equation and modular forms of weight one, to appear in Nagoya Math. J., 100(1985).
5) H. Ishii, On the coincidence of L-functions, (preprint).
6) M. Jimbo and T. Miwa, Irreducible decomposition of fundamental modules for C⁽¹⁾_l and C⁽¹⁾_l, and Hecke modular forms, Publ. Res. Inst. Math. Sci., 434, Kyoto University, 1983.
7) V. G. Kac and D. H. Peterson, Infinite-dimensional Lie algebras, theta functions and modular forms, Adv. in Math., 53 (1984), 125-254.
8) F. Halter-Koch, Arithmetische Theorie der Normkörper von 2-Potenzgrad mit Diedergruppe, J. Number Theory, 3 (1971), 412-443.
9) M. Koike, On McKay's conjecture, Nagoya Math. J., 95 (1984), 85-89.
10) G. Lion and M. Vergne, The Weil representation, Maslov index and theta series, Birkhäuser, Boston, 1980.
11) H. Petersson, Modulfunktionen und quadratische Formen, Springer-Verlag, Berlin and Heidelberg, 1982.
12) J-P. Serre, Modular forms of weight one and Galois representations, Proc. Symposium on Algebraic Number Fields, Academic Press, London, 1977, 193-268.
13) T. Shintani, On certain ray class invariants of real quadratic fields, J. Math. Soc. Japan, 30 (1978), 139-167.

Right : [1] E. Hecke, Über einen neuen Zusammenhang zwischen elliptischen Modulfunktionen und indefiniten quadratischen Formen, Mathematische Werke, Vandenhoeck & Ruprecht, Göttingen, 1959, 418-427.
[2] E. Hecke, Zur Theorie der elliptischen Modulfunktionen, Mathematische Werke, Vandenhoeck & Ruprecht, Göttingen, 428-460.
[3] T. Hiramatsu, Higher reciprocity laws and modular forms of weight one, Comm. Math. Univ. St. Paul., 31 (1982), 75-85.
[4] T. Hiramatsu and Y. Mimura, The modular equation and modular forms of weight one, to appear in Nagoya Math. J., 100 (1985).
[5] H. Ishii, On the coincidence of L-functions, (preprint).
[6] M. Jimbo and T. Miwa, Irreducible decomposition of fundamental modules for A⁽¹⁾_l and C⁽¹⁾_l, and Hecke modular forms, Publ. Res. Inst. Math. Sci., 434, Kyoto University, 1983.
[7] V. G. Kac and D. H. Peterson, Infinite-dimensional Lie algebras, theta functions and modular forms, Adv. in Math., 53 (1984), 125-254.
[8] F. Halter-Koch, Arithmetische Theorie der Normkörper von 2-Potenzgrad mit Diedergruppe, J. Number Theory, 3 (1971), 412-443.
[9] M. Koike, On McKay's conjecture, Nagoya Math. J., 95 (1984), 85-89.
[10] G. Lion and M. Vergne, The Weil representation, Maslov index and theta series, Birkhäuser, Boston, 1980.
[11] H. Petersson, Modulfunktionen und quadratische Formen, Springer-Verlag, Berlin and Heidelberg, 1982.
[12] J-P. Serre, Modular forms of weight one and Galois representations, Proc. Symposium on Algebraic Number Fields, Academic Press, London, 1977, 193-268.
[13] T. Shintani, On certain ray class invariants of real quadratic fields, J. Math. Soc. Japan, 30 (1978), 139-167.

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