On Qab-rationality of Eisenstein series of weight 3/2

Toshitsune MIYAKE

doi:10.2969/jmsj/04130473

On Q_ab-rationality of Eisenstein series of weight 3/2

Toshitsune MIYAKE

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JOURNAL FREE ACCESS

1989 Volume 41 Issue 3 Pages 473-492

DOI https://doi.org/10.2969/jmsj/04130473

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Published: 1989 Received: April 27, 1988 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, Theorie der Eisensteinschen Reihen höherer Stufe und ihre Anwendung auf Funktionentheorie und Arithmetik, Abh. Math. Sem. Univ. Hamburg, 5(1927), 199-224 (Werke, No. 24).
2) T. Miyake, Modular Forms, Springer (to appear).
3) T.-Y. Pei, Eisenstein series of weight 3/2: I, II, Trans. Amer. Math. Soc., 274 (1982), 573-606, 283 (1984), 589-603.
4) G. Shimura, On modular forms of half integral weight, Ann. of Math., 97 (1973), 440-481.
5) G. Shimura, On the holomorphy of certain Dirichlet series, Proc. London Math. Soc., 31 (1975), 79-98.
6) G. Shimura, Theta functions with complex multiplication, Duke Math. J., 43 (1976), 673-696.
7) G. Shimura, Confluent hypergeometric functions on tube domains, Math. Ann., 260 (1982), 269-302.
8) G. Shimura, On Eisenstein series of half-integral weight, Duke Math. J., 52 (1985), 281-314.
9) G. Shimura, On the Eisenstein series of Hilbert modular groups, Rev. Mat. Iberoamericana, 1 (1985), 1-42.
10) J. Sturm, Special values of zeta functions and Eisenstein series of half integral weight, Amer. J. Math., 102 (1980), 219-240, 781-783.

Right : [1] E. Hecke, Theorie der Eisensteinschen Reihen höherer Stufe und ihre Anwendung auf Funktionentheorie und Arithmetik, Abh. Math. Sem. Univ. Hamburg, 5 (1927), 199-224 (Werke, No. 24).
[2] T. Miyake, Modular Forms, Springer (to appear).
[3] T. -Y. Pei, Eisenstein series of weight 3/2: I, II, Trans. Amer. Math. Soc., 274 (1982), 573-606, 283 (1984), 589-603.
[4] G. Shimura, On modular forms of half integral weight, Ann. of Math., 97 (1973), 440-481.
[5] G. Shimura, On the holomorphy of certain Dirichlet series, Proc. London Math. Soc., 31 (1975), 79-98.
[6] G. Shimura, Theta functions with complex multiplication, Duke Math. J., 43 (1976), 673-696.
[7] G. Shimura, Confluent hypergeometric functions on tube domains, Math. Ann., 260 (1982), 269-302.
[8] G. Shimura, On Eisenstein series of half-integral weight, Duke Math. J., 52 (1985), 281-314.
[9] G. Shimura, On the Eisenstein series of Hilbert modular groups, Rev. Mat. Iberoamericana, 1 (1985), 1-42.
[10] J. Sturm, Special values of zeta functions and Eisenstein series of half integral weight, Amer. J. Math., 102 (1980), 219-240, 781-783.

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

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