Duke Mathematical Journal

On Eisenstein series of half-integral weight

Goro Shimura

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J., Volume 52, Number 2 (1985), 281-314.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077304434

Digital Object Identifier
doi:10.1215/S0012-7094-85-05216-0

Mathematical Reviews number (MathSciNet)
MR792175

Zentralblatt MATH identifier
0577.10025

Subjects
Primary: 11F41: Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]
Secondary: 11F37: Forms of half-integer weight; nonholomorphic modular forms 11M41: Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}

Citation

Shimura, Goro. On Eisenstein series of half-integral weight. Duke Math. J. 52 (1985), no. 2, 281--314. doi:10.1215/S0012-7094-85-05216-0. https://projecteuclid.org/euclid.dmj/1077304434


Export citation

References

  • [1] H. Bass, J. Milnor, and J.-P. Serre, Solution of the congruence subgroup problem for ${\rm SL}\sb{n}\,(n\geq 3)$ and ${\rm Sp}\sb{2n}\,(n\geq 2)$, Inst. Hautes Études Sci. Publ. Math. (1967), no. 33, 59–137.
  • [2] P. Feit, Finiteness and analyticity of Eisenstein series, Thesis, Princeton University, 1985.
  • [3] Y. Kitaoka, Dirichlet series in the theory of Siegel modular forms, Nagoya Math. J. 95 (1984), 73–84.
  • [4] R. P. Langlands, On the functional equations satisfied by Eisenstein series, Lecture Notes in Mathematics, vol. 544, Springer-Verlag, Berlin, 1976.
  • [5] H. Maass, Konstruktion ganzer Modulformen halbzahliger Dimension mit $\theta$-Multiplikatoren in einer und zwei Variablen, Abh. Math. Sem. Hamburg 12 (1937), 134–162.
  • [6] H. Maass, Konstruktion ganzer Modulformen halbzahliger Dimension mit $\theta$-Multiplikatoren in zwei Variablen., Math. Z. 43 (1938), 709–738 (German).
  • [7]1 T.-Y. Pei, Eisenstein series of weight $3/2$. I, Trans. Amer. Math. Soc. 274 (1982), no. 2, 573–606.
  • [7]2 T.-Y. Pei, Eisenstein series of weight ${3\over 2}$. II, Trans. Amer. Math. Soc. 283 (1984), no. 2, 589–603.
  • [8] H. Petersson, Über die Entwicklungskoeffizienten der ganzen Modulformen und ihre Bedeutung für die zahlentheorie, Abh. Math. Sem. Hamburg 8 (1931), 215–242.
  • [9] G. Shimura, On modular forms of half integral weight, Ann. of Math. (2) 97 (1973), 440–481.
  • [10] G. Shimura, On the holomorphy of certain Dirichlet series, Proc. London Math. Soc. (3) 31 (1975), no. 1, 79–98.
  • [11] G. Shimura, Theta functions with complex multiplication, Duke Math. J. 43 (1976), no. 4, 673–696.
  • [12] G. Shimura, The arithmetic of certain zeta functions and automorphic forms on orthogonal groups, Ann. of Math. (2) 111 (1980), no. 2, 313–375.
  • [13]1 G. Shimura, On certain zeta functions attached to two Hilbert modular forms. I. The case of Hecke characters, Ann. of Math. (2) 114 (1981), no. 1, 127–164.
  • [13]2 G. Shimura, On certain zeta functions attached to two Hilbert modular forms. II. The case of automorphic forms on a quaternion algebra, Ann. of Math. (2) 114 (1981), no. 3, 569–607.
  • [14] G. Shimura, Confluent hypergeometric functions on tube domains, Math. Ann. 260 (1982), no. 3, 269–302.
  • [15] G. Shimura, On Eisenstein series, Duke Math. J. 50 (1983), no. 2, 417–476.
  • [16] G. Shimura, Algebraic relations between critical values of zeta functions and inner products, Amer. J. Math. 105 (1983), no. 1, 253–285.
  • [17] C. L. Siegel, On the theory of indefinite quadratic forms, Ann. of Math. (2) 45 (1944), 577–622.
  • [18] C. L. Siegel, Die Funktionalgleichungen einiger Dirichletscher Reihen, Math. Z. 63 (1956), 363–373.
  • [19] J. Sturm, Special values of zeta functions, and Eisenstein series of half integral weight, Amer. J. Math. 102 (1980), no. 2, 219–240.
  • [20] A. Weil, Sur certains groupes d'opérateurs unitaires, Acta Math. 111 (1964), 143–211.