The critical values of certain zeta functions associated with modular forms of half-integral weight

Goro SHIMURA

doi:10.2969/jmsj/03340649

Goro SHIMURA

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JOURNAL FREE ACCESS

1981 Volume 33 Issue 4 Pages 649-672

DOI https://doi.org/10.2969/jmsj/03340649

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Published: 1981 Received: March 24, 1980 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) Y. Flicker, Automorphic forms on covering groups of GL (2), preprint, 1979.
2) S. Gelbart and I. Piatetski-Shapiro, On Shimura's correspondence for modular forms of half-integral weight, Proc. Int. Coll., Bombay, 1979.
3) T. Miyake, On automorphic forms on GL₂ and Hecke operators, Ann. of Math., 94 (1971), 174-189.
4) S. Niwa, Modular forms of half integral weight and the integral of certain theta-functions, Nagoya Math. J., 56 (1975), 147-161.
5) H. Petersson, Über die Entwicklungskoeffizienten der ganzen Modulformen und ihre Bedeutung für die Zahlentheorie, Abh. Math. Sem. Univ. Hamburg, 8 (1931), 215-242.
6) H. Petersson, Über die systematische Bedeutung der Eisensteinschen Reihen, Abh. Math. Sem. Univ. Hamburg, 16 (1949), 104-130.
7) J.-P. Serre and H. Stark, Modular forms of weight 1/2, Modular functions of one variable VI, Lecture Notes in Math., 627 (1977), Springer, 27-67.
8) G. Shimura, Introduction to the arithmetic theory of automorphic functions, Publ. Math. Soc. Japan, No. 11, Iwanami Shoten and Princeton Univ. Press, 1971.
9) G. Shimura, On modular forms of half integral weight, Ann. of Math., 97 (1973), 440-481.
10) G. Shimura, On the holomorphy of certain Dirichlet series, Proc. London Math. Soc., 31 (1975), 79-98.
11) G. Shimura, Theta functions with complex multiplication, Duke Math. J., 43(1976), 673-696.
12) G. Shimura, The special values of the zeta functions associated with cusp forms, Comm. Pure Appl. Math., 29(1976), 783-804.
13) G. Shimura, On the periods of modular forms, Math. Ann., 229 (1977), 211-221.
14) G. Shimura, The special values of the zeta functions associated with Hilbert modular forms, Duke Math. J., 45 (1978), 637-679.
15) G. Shimura, On certain reciprocity-laws for theta functions and modular forms, Acta Math., 141 (1978), 35-71.
16) T. Shintani, On construction of holomorphic cusp forms of half integral weight, Nagoya Math. J., 58 (1975), 83-126.
17) J. Sturm, Special values of zeta functions and Eisenstein series of half integral weight, Amer. J. Math., 102 (1980), 219-240.
18) J. Sturm, Addendum to special values of zeta functions, Amer. J. Math., 102 (1980), 781-783.

Right : [1] Y. Flicker, Automorphic forms on covering groups of GL(2), preprint, 1979.
[2] S. Gelbart and I. Piatetski-Shapiro, On Shimura's correspondence for modular forms of half-integral weight, Proc. Int. Coll., Bombay, 1979.
[3] T. Miyake, On automorphic forms on GL₂ and Hecke operators, Ann. of Math., 94 (1971), 174-189.
[4] S. Niwa, Modular forms of half integral weight and the integral of certain theta-functions, Nagoya Math. J., 56 (1975), 147-161.
[5] H. Petersson, Über die Entwicklungskoeffizienten der ganzen Modulformen und ihre Bedeutung für die Zahlentheorie, Abh. Math. Sem. Univ. Hamburg, 8 (1931), 215-242.
[6] H. Petersson, Über die systematische Bedeutung der Eisensteinschen Reihen, Abh. Math. Sem. Univ. Hamburg, 16 (1949), 104-130.
[7] J. -P. Serre and H. Stark, Modular forms of weight 1/2, Modular functions of one variable VI, Lecture Notes in Math., 627 (1977), Springer, 27-67.
[8] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Publ. Math. Soc. Japan, No. 11, Iwanami Shoten and Princeton Univ. Press, 1971.
[9] G. Shimura, On modular forms of half integral weight, Ann. of Math., 97 (1973), 440-481.
[10] G. Shimura, On the holomorphy of certain Dirichlet series, Proc. London Math. Soc., 31 (1975), 79-98.
[11] G. Shimura, Theta functions with complex multiplication, Duke Math. J., 43 (1976), 673-696.
[12] G. Shimura, The special values of the zeta functions associated with cusp forms, Comm. Pure Appl. Math., 29 (1976), 783-804.
[13] G. Shimura, On the periods of modular forms, Math. Ann., 229 (1977), 211-221.
[14] G. Shimura, The special values of the zeta functions associated with Hilbert modular forms, Duke Math. J., 45 (1978), 637-679.
[15] G. Shimura, On certain reciprocity-laws for theta functions and modular forms, Acta Math., 141 (1978), 35-71.
[16] T. Shintani, On construction of holomorphic cusp forms of half integral weight, Nagoya Math. J., 58 (1975), 83-126.
[17] J. Sturm, Special values of zeta functions and Eisenstein series of half integral weight, Amer. J. Math., 102 (1980), 219-240.
[18] J. Sturm, Addendum to special values of zeta functions, Amer. J. Math., 102 (1980), 781-783.

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