# Shimura correspondence of Maass wave forms of half integral weight

Acta Arithmetica (1995)

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

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top## How to cite

topHisashi 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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- [2] K. Doi and T. Miyake, Automorphic Forms and Number Theory, Kinokuniya Book Store, 1974 (in Japanese). Zbl0466.10012
- [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] S. Friedberg, On Maass wave forms and the imaginary quadratic Doi-Naganuma lifting, Math. Ann. 263 (1983), 483-508. Zbl0497.10019
- [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] D. A. Hejhal, Some Dirichlet series with coefficients related to periods of automorphic eigenforms, Proc. Japan Acad. 58 (1982), 413-417. Zbl0516.10018
- [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] T. Oda, On modular forms associated with indefinite quadratic forms of signature (2,n-2), Math. Ann. 231 (1978), 97-144. Zbl0346.10013
- [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] P. Sarnak, Additive number theory and Maass forms, Lecture Notes in Math. 1052, Springer, Berlin, 1984, 286-309. Zbl0534.10021
- [11] G. Shimura, On modular forms of half integral weight, Ann. of Math. 97 (1973), 440-481. Zbl0266.10022
- [12] T. Shintani, On construction of holomorphic cusp forms of half integral weight, Nagoya Math. J. 58 (1975), 83-126. Zbl0316.10016
- [13] J.-L. Waldspurger, Correspondence de Shimura, J. Math. Pures Appl. 59 (1980), 1-133.

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