Duke Mathematical Journal

On Hilbert modular forms of half-integral weight

Goro Shimura

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Article information

Source
Duke Math. J. Volume 55, Number 4 (1987), 765-838.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077306298

Digital Object Identifier
doi:10.1215/S0012-7094-87-05538-4

Mathematical Reviews number (MathSciNet)
MR916119

Zentralblatt MATH identifier
0636.10024

Subjects
Primary: 11F37: Forms of half-integer weight; nonholomorphic modular forms
Secondary: 11F41: Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20] 11F66: Langlands $L$-functions; one variable Dirichlet series and functional equations 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols

Citation

Shimura, Goro. On Hilbert modular forms of half-integral weight. Duke Math. J. 55 (1987), no. 4, 765--838. doi:10.1215/S0012-7094-87-05538-4. http://projecteuclid.org/euclid.dmj/1077306298.


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References

  • [B] V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform, Comm. Pure Appl. Math. 14 (1961), 187–214.
  • [F] Y. Flicker, Automorphic forms on covering groups of $\rm GL(2)$, Invent. Math. 57 (1980), no. 2, 119–182.
  • [GP1] S. Gelbart and I. Piatetski-Shapiro, On Shimura's correspondence for modular forms of half-integral weight, Automorphic Forms, Representation Theory and Arithmetic (Bombay, 1979), Tata Inst. Fund. Res. Studies in Math., vol. 10, Tata Inst. Fundamental Res., Bombay, 1981, pp. 1–39.
  • [GP2] S. Gelbart and I. Piatetski-Shapiro, Some remarks on metaplectic cusp forms and the correspondences of Shimura and Waldspurger, Israel J. Math. 44 (1983), no. 2, 97–126.
  • [I] J. Igusa, Theta Functions, Springer, New York, 1972.
  • [M] T. Miyake, On automorphic forms on $\rm GL\sb2$ and Hecke operators, Ann. of Math. (2) 94 (1971), 174–189.
  • [N] S. Niwa, Modular forms of half integral weight and the integral of certain theta-functions, Nagoya Math. J. 56 (1975), 147–161.
  • [P]1 T-y. Pei, Eisenstein series of weight $3/2$. I, Trans. Amer. Math. Soc. 274 (1982), no. 2, 573–606.
  • [P]2 T-y. Pei, Eisenstein series of weight $3\over 2$: II, Trans. Amer. Math. Soc. 283 (1984), no. 2, 589–603.
  • [SS] J.-P. Serre and H. M. Stark, Modular forms of weight $1/2$, Modular Functions of One Variable, VI (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976), Lecture Notes in Math., vol. 627, Springer, Berlin, 1977, pp. 27–67.
  • [S1] G. Shimura, On modular forms of half integral weight, Ann. of Math. (2) 97 (1973), 440–481.
  • [S2] G. Shimura, On the periods of modular forms, Math. Ann. 229 (1977), no. 3, 211–221.
  • [S3] G. Shimura, The special values of the zeta functions associated with Hilbert modular forms, Duke Math. J. 45 (1978), no. 3, 637–679.
  • [S4] G. Shimura, The arithmetic of certain zeta functions and automorphic forms on orthogonal groups, Ann. of Math. (2) 111 (1980), no. 2, 313–375.
  • [S5]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.
  • [S5]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.
  • [S6] G. Shimura, The critical values of certain zeta functions associated with modular forms of half-integral weight, J. Math. Soc. Japan 33 (1981), no. 4, 649–672.
  • [S7] G. Shimura, On Eisenstein series, Duke Math. J. 50 (1983), no. 2, 417–476.
  • [S8] G. Shimura, On Eisenstein series of half-integral weight, Duke Math. J. 52 (1985), no. 2, 281–314.
  • [S9] G. Shimura, On the Eisenstein series of Hilbert modular groups, Rev. Mat. Iberoamericana 1 (1985), no. 3, 1–42.
  • [S10] G. Shimura, On a class of nearly holomorphic automorphic forms, Ann. of Math. (2) 123 (1986), no. 2, 347–406.
  • [S11] G. Shimura, Nearly holomorphic functions on hermitian symmetric spaces, to appear in Math. Ann.
  • [St] J. Sturm, Theta series of weight $3/2$, J. Number Theory 14 (1982), no. 3, 353–361.
  • [Wa] J.-L. Waldspurger, Correspondance de Shimura, J. Math. Pures Appl. (9) 59 (1980), no. 1, 1–132.
  • [We] A. Weil, Sur certains groupes d'opérateurs unitaires, Acta Math. 111 (1964), 143–211.