Remark on Fourier coefficients of modular forms of half integral weight belonging to Kohnen's spaces

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概要

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• The purpose of this paper is to derive that the square of Fourier coefficients a(n) at a square free positive integer n of modular forms f of half integral weight belonging to Kohnens 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 F of integral weight which is the image of f under the Shimura correspondence. Previously, Kohnen-Zagier had obtained an analogous result in the case of Kohnens spaces of square free level and of trivial character. Our results give some generalizations of them of Kohnen-Zagier. Our method of the proof is similar to that of Shimuras paper concerning Fourier coefficients of Hilbert modular forms of half integral weight over totally real fields.

• 社団法人 日本数学会の論文

著者

• Kojima Hisashi

  Department Of Mathematics The University Of Electro-communications

• Kojima Hisashi

  Department Of Mathematics Faculty Of Education Iwate University

• Kojima Hisashi

  Department of Chemistry, Nagoya Institute of Technology

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