Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 51, Number 3 (1999), 715-730.
Remark on Fourier coefficients of modular forms of half integral weight belonging to Kohnen's spaces
The purpose of this paper is to derive that the square of Fourier coefficients at a square free positive integer of modular forms of half integral weight belonging to Kohnen's spaces of arbitrary odd level and of arbitrary primitive character is essentially equal to the critical value of the zeta function attached to the modular form of integral weight which is the image of under the Shimura correspondence. Previously, KohnenZagier had obtained an analogous result in the case of Kohnen's spaces of square free level and of trivial character. Our results give some generalizations of them of KohnenZagier. Our method of the proof is similar to that of Shimura's paper concerning Fourier coefficients of Hilbert modular forms of half integral weight over totally real fields.
J. Math. Soc. Japan, Volume 51, Number 3 (1999), 715-730.
First available in Project Euclid: 10 June 2008
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11F37: Forms of half-integer weight; nonholomorphic modular forms
Secondary: 11F30: Fourier coefficients of automorphic forms 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
KOJIMA, Hisashi. Remark on Fourier coefficients of modular forms of half integral weight belonging to Kohnen's spaces. J. Math. Soc. Japan 51 (1999), no. 3, 715--730. doi:10.2969/jmsj/05130715. https://projecteuclid.org/euclid.jmsj/1213107913