Shimura correspondence of Maass wave forms of half integral weight

Hisashi Kojima

Acta Arithmetica (1995)

  • Volume: 69, Issue: 4, page 367-385
  • ISSN: 0065-1036

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Hisashi Kojima. "Shimura correspondence of Maass wave forms of half integral weight." Acta Arithmetica 69.4 (1995): 367-385. <http://eudml.org/doc/206693>.

@article{HisashiKojima1995,
author = {Hisashi Kojima},
journal = {Acta Arithmetica},
keywords = {Maass wave forms; Shimura correspondence; nonholomorphic modular forms; half-integral weight; Fourier coefficients; Hecke operators},
language = {eng},
number = {4},
pages = {367-385},
title = {Shimura correspondence of Maass wave forms of half integral weight},
url = {http://eudml.org/doc/206693},
volume = {69},
year = {1995},
}

TY - JOUR
AU - Hisashi Kojima
TI - Shimura correspondence of Maass wave forms of half integral weight
JO - Acta Arithmetica
PY - 1995
VL - 69
IS - 4
SP - 367
EP - 385
LA - eng
KW - Maass wave forms; Shimura correspondence; nonholomorphic modular forms; half-integral weight; Fourier coefficients; Hecke operators
UR - http://eudml.org/doc/206693
ER -

References

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  1. [1] T. Asai, On the Doi-Naganuma lifting associated with imaginary quadratic fields, Nagoya Math. J. 71 (1978), 149-167. Zbl0357.10013
  2. [2] K. Doi and T. Miyake, Automorphic Forms and Number Theory, Kinokuniya Book Store, 1974 (in Japanese). Zbl0466.10012
  3. [3] S. Friedberg, On the imaginary quadratic Doi-Naganuma lifting of modular forms of arbitrary level, Nagoya Math. J. 92 (1983), 1-20. Zbl0506.10022
  4. [4] S. Friedberg, On Maass wave forms and the imaginary quadratic Doi-Naganuma lifting, Math. Ann. 263 (1983), 483-508. Zbl0497.10019
  5. [5] S. Gelbert and I. Piatetski-Shapiro, On Shimura's correspondence for modular forms of half-integral weight, in: Proc. Internat. Colloq. Automorphic Forms, Representation Theory and Arithmetic, 1979, Tata Institute, Springer, 1981, 1-39. 
  6. [6] D. A. Hejhal, Some Dirichlet series with coefficients related to periods of automorphic eigenforms, Proc. Japan Acad. 58 (1982), 413-417. Zbl0516.10018
  7. [7] S. Niwa, Modular forms of half integral weight and the integral of certain theta-functions, Nagoya Math. J. 56 (1974), 147-161. Zbl0303.10027
  8. [8] T. Oda, On modular forms associated with indefinite quadratic forms of signature (2,n-2), Math. Ann. 231 (1978), 97-144. Zbl0346.10013
  9. [9] S. Rallis and G. Schiffmann, On a relation between S͠L cusp forms and cusp forms on tube domains associated to orthogonal groups, Trans. Amer. Math. Soc. 263 (1981), 1-58. Zbl0465.10024
  10. [10] P. Sarnak, Additive number theory and Maass forms, Lecture Notes in Math. 1052, Springer, Berlin, 1984, 286-309. Zbl0534.10021
  11. [11] G. Shimura, On modular forms of half integral weight, Ann. of Math. 97 (1973), 440-481. Zbl0266.10022
  12. [12] T. Shintani, On construction of holomorphic cusp forms of half integral weight, Nagoya Math. J. 58 (1975), 83-126. Zbl0316.10016
  13. [13] J.-L. Waldspurger, Correspondence de Shimura, J. Math. Pures Appl. 59 (1980), 1-133. 

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